#arithmetic progression questions

[9nid]

📘 JEE Series Part-18 | Arithmetic Progression (AP) Part-02 – Deep Dive into Core Concepts

Welcome to Part-18 of the 9nid JEE Series, your ultimate Hinglish learning zone for mastering JEE Maths with clarity and confidence. In this session, we go deeper into Arithmetic Progression (AP) — one of the most scoring topics in Sequence and Series for JEE Main and Advanced. 🔍 What’s Covered in This Video? In this video, we move beyond the basics of AP and explore more conceptual and…

[edusquaremaths]

📘 JEE Series Part-18 | Arithmetic Progression (AP) Part-02 – Deep Dive into Core Concepts

Welcome to Part-18 of the 9nid JEE Series, your ultimate Hinglish learning zone for mastering JEE Maths with clarity and confidence. In this session, we go deeper into Arithmetic Progression (AP) — one of the most scoring topics in Sequence and Series for JEE Main and Advanced. 🔍 What’s Covered in This Video? In this video, we move beyond the basics of AP and explore more conceptual and…

[insight-chronicles]

Chapter 5 - Is this the end?

Word Count: 3.2 Content Warning: Swearing Summary: Is everything you’ve worked so hard to conceal about to come to light? Plus a little bonus Jinwoo POV

Authors Note: Thought I would try something, I added a little bit of Jinwoo POV at the end of this chapter, let me know what you think and if that’s something you want me to continue try to add sporadically as it makes sense.

AO3

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Masterlist

Dodging all the questions and making sure you weren’t followed was harder then you had expected so it had taken you longer to get home then you’d wanted. After finally locking your front door you collapsed onto the bed still in your hunters gear, you’d worry about the blood stains on your bedding tomorrow. You slept hard that night, so deep was your sleep, in fact, that you’d completely ignored your alarm this morning. Jolting awake at a car horn just outside your window you looked over at the clock on your nightstand. Shit, was that really the time!? Some quick mental arithmetic said if you rushed and skipped breakfast you should still be able to make it to work in time, you always set your alarm nice and early so you had a nice leisurely time to wake up and get ready, you hated nothing more than being rushed.

You’d made it, slightly dishevelled and stomach rubbing, but you made it. Luckily you had a slow day and you planned on just catching up on some paperwork so you could spare a few minutes to got to the breakroom to get a cup of caffeine and a pastry to tide you over until you could get some lunch.

As you found out that day, there was no such thing as enough caffeine to make a report bearable when all you wanted to do was go back to bed. Thankfully the report was not urgent so it didn’t matter that you had been yawning at your screen all morning and making no progress whatsoever. Although all those trips to the breakroom for more caffeine had meant you had overheard some rumours that set you on edge.

There was a knock on your office door, not that you heard it having mastered the art of falling asleep with your eyes open that morning. You didn’t even notice the cause of the knock entering the room and clearing their throat in front of your desk. In fact it wasn’t until they leant over the desk and tapped the back of your hand where it lay on your mouse, that you noticed the intruder. You startled from your half sleeping state to see Chief Inspector Woo straightening up.

“Sorry about that. I didn’t mean to startle you, I did try knocking but you were so engrossed in your work you didn’t notice.” There was a hint of admiration in his tone, you felt your cheeks heat with embarrassment at the undeserved praise. Usually when Jinchul visited you there was a cheerful, friendliness to his tone that was missing today, replaced with a hardness that suggested he was here on official business not a personal call.

“Oh, um, sorry. Was just, yeah, concentrating.” His sudden appearance and seriousness was making you stumble over your words, “What can I do for you Chief Inspector?” You tried to match his formalness but it felt odd on your tongue. Taking your eyes off him you save the document and make sure to close down the application before returning your gaze to him, giving  him your full attention. Whatever this was about you were sure you would be leaving this office, you just hoped that it wasn’t about the rumours circulating, it would be just your luck at the moment that the party you’d worked with last night couldn’t keep a secret for even 24 hours.

“You're needed for a meeting with the Chairman.” Jinchul straightened his tie, his straight to the point no nonsense approach to this conversation had your hackles raising.

“Can I ask what the meeting is about?” Whilst there was legitimate reasons that you would need to see the Chairman you could not see why the summoning would need to be so formal.

“That’s confidential I’m afraid. The topic cannot be discussed outside of Chairman Go’s office.” You felt yourself visibly, and probably audibly, gulp. It was never a good sign when officials got cryptic.

“Right, well, I’ll be up as soon as I am finished with this piece of work.” You gesture to the blank screen in front of you, silently cursing yourself for already having closed everything down.

“Your presence is required immediately.”

“Right now?” Jinchul nods. Well then, guess I don’t have a choice. You take a deep breath nodding your head slowly as you make a show of turning off your computer. Standing you wipe your sweaty palms down the fronts of your trousers, both drying your hands and smoothing out the creases that had formed from being at your desk all day.

Rounding your desk you follow Jincul out of the room, pausing to shut and lock the door behind you. Jinchul says nothing as he leads you to the elevator, stepping inside you lean against the back wall while he stands to attention near the centre.

Your upwards journey is paused at the lobby where the doors open to admit 2 more passengers into the cramped space. Baek Yoonho and Choi Jongin. Both smile at you as they walk in but the smiles quickly drop from their faces as they take in the worried expression on yours. Whilst you had not had many personal interactions with Jongin he had been to your office enough to scout new hunters and discuss the possibility of poaching others from rival guilds. He had insisted almost from the first meeting that you call him Jongin, even now it felt weird. Yoonho on the other hand has been even more attentive and protective of you since your disaster of a date. Great, stuck in a cramped space with 3 guys with egos the size of Mars and all protective of little old me, this is exactly what I needed today. Not.

“Hey, Y/N, are you alright?” Yoonho skirts around Jinchul, shooting daggers at him with his eyes as he does, he comes to a stop in front of you. You nod in response but you don’t trust yourself to speak. Whatever he saw in your eyes put him on edge, he reached up to grip your shoulders almost harshly. Before he could speak, Jongin's voice cut through.

“What’s going on here?” The question was directed at the Chief Inspector but Jongin was looking at you.

“Just heading up for a meeting with Chairman Go.” Jinchul replies nonchalantly, shrugging.

“Then why does she look like she's about to walk in front of a firing squad?” Jongin gestures at you, his fiery gaze cutting to Jinchul. Looking over his shoulder at you Jinchul is surprised by what he sees.

“I have no idea.” Turning his whole body to face you, a wave of confusion and concern clouds all other emotions. All three of these men feeling the same thing in such a confined space is making it hard to block out. “Y/N, what's the matter? You’ve met with Go many times, why are you so worried?” You shake your head and shrug, dislodging Yoonho's hands from where they still rest on your shoulders.

“I don’t know.” Your voice is weak.”This just feels different. You came into my office all serious and have barely said a word to me, being all cryptic and shit. Only telling me we can’t talk about it outside Go;s office and that it needed to happen right now. What am I supposed to think?” The words come out fast and garbled together, you're surprised they understand you.

“Go just wants to discuss the progress of your assignment, that's all.” Jinchul tried to comfort you but his efforts were thwarted by Yoonho and Jongins reaction to the news.

“What assignment?” Jongin was curious as to what the Chairman could be getting as an office worker or do that required classified updates.

What have you gotten her into?” Yoonho was just plain mad. You knew Jinchul would have to choose his next words carefully or risk Yoonho’s tiger coming to the surface. “Wait, has this got something to do with why you were upset leaving Go’s office the other week?” You can feel Yoonhos power emanating from him, you nod slowly hoping you don’t cause him to tip past the point of control.

“I’m afraid I’m not at liberty to say. Whilst I am aware of the assignment I cannot discuss it. Although I can tell you it is perfectly safe and should pose no risk to Y/N health.” Jinchul held his hands up almost in surrender. Yoonho relaxed slightly, the glow of his eyes dimming but you could tell from the tension in his muscles he was still ready for a fight.

“We’re coming with you.” You weren’t expecting that to come from Jongin, Yoonho sure, that was exactly the sort of thing he thought he could get away with as a S-Rank Hunter and Guild Master. But Jongin always seemed so cool and calculated but this came across as more of a rash move on his part, one that could potentially land him on the bad side of the Chairman.

“I can’t allow that.” Jinchul knew he couldn’t make the two S-Ranks do anything but he hoped if he reminded them of the rules they would fall in line.

“You don’t have to allow it.”

“We are going with her.” Yoonho cut in, an unspoken threat in his voice. Jinchul’s eyes met yours with a look you couldn’t decipher, it was more than just concern.

The four of you entered Chairman Go’s office. Jinchul leads the way, you following just behind with Yoonho and Jongin flanking you like bodyguards. Chairman Go looks up from the file in his hands, surprised by the number of people suddenly in his office.

“My apologies, sir, but when we met in the elevator they insisted on coming.” Jinchul bowed his head.

“Right,” Chairman Go started, “Do they - “ He trailed off, communicating the rest of his sentence with his eyes.

“No, sir”

Clearing his throat, Go straightened some papers on his desk. You felt a wave of unease from him. The Chairman was always such a confident man, it made you wonder how he thought the men flanking you would react to the news he was obviously about to share with them.

“As it seems that you two have latched yourselves onto Miss L/N, I suppose it can’t do much harm to let you know what her assignment is.” His voice is calm and authoritative, much more like the Chairman Go everybody knows and looks up to. “After all you would be partial to the information she gathers eventually anyway.”

“What information?” Jongin steps forward so he now stands between you and the Chairman's desk. Yoonho rests his hand on your lower back as if to remind you he’s there for you if you need him. Go’s eyes lock on to the movement before meeting yours with a raised, questioning eyebrow. You returned his question with a subtle shake of your head.

“Before I tell you anything I need you to understand that it is the role of the Hunters Association to gather information on all hunters.” The men nod, murmuring their understanding, “I have given Y/N here the task of getting close to Hunter Sung so we can find out more about his power. Of course, both of your statements regarding the raid on Jeju Island were invaluable,as were all the statements. But it is my belief there is still more to Sungs power then we know. It is my belief that he is one of, if not the, strongest hunter to grace South Korean soil, if not the world. And he just seems to keep getting stronger. We need to know more” Chairman Go rests his elbows on the desk, steepling his fingers, waiting for their response. Jongin stands frozen. You feel Yoonho’s fingers dig into your lower back, your sure it would hurt a human so you fake a flinch.

“You’re using an analyst as a spy?” Yoonho’s voice is low and dangerous.

“She is in no danger.”

“You don’t know that! You just said yourself that you don't know what Sung is capable of!” Yoonho releases you and storms forward, slamming his fists onto the desk, threatening to split it in two.

“Sung could be the biggest threat this country has ever seen! And you think sending someone from the archives is the best way to get information from him?” Jongin snaps out of his daze, just as mad as Yoonho. Flames dance along his shoulders just waiting to be released and he struggles to keep his power in check.

“I can’t believe this. What was the plan if Sung found out what you were up to and took his anger out on her?”

“Shut up.” You could let them yell at each other all day about the morals of using you for this assignment but you could not stand them dragging Jinwoo's name through the mud like that. They were still yelling. “I said SHUT UP!” you matched their level. This time they felt quiet turning to you as if they forgot you were even in the room. “Stop talking about me like I'm not in the room. Stop implying the only way this can end is with me getting hurt. Stop assuming I’m some damsel that needs saving or protecting. And most of all stop saying Jinwoo is going to hurt me. I know him. He may not remember me, but I know him and he would never, and I mean never hurt me!” You stand there chest heaving when suddenly the reality of what you just revealed hits you.

You bolt from the room.

Panting you skid to a halt at your front door. What have you done? Have you just ruined everything? The perfectly constructed narrative you've worked so hard for over the last few years, is it all gone? Fumbling you insert the key into the door. You would bet you had around an hour before someone shows up at your door.

There was no getting out of this. There was no possible explanation you could give as to why you knew Jinwoo that wouldn’t reveal things you didn't want people to know. You collapsed onto the sofa, you’d fucked everything up.

There was a knock on the door. You looked at your watch, yep right on time. Pulling yourself up from the sofa you walk over to open the door. Turning and walking over to the kitchen you let the door swing open. Jongin stands on the other side of the threshold unsure if he's allowed into your apartment or not. Suddenly he jerks forward as Yoonho storms through the door, furious eyes searching for you before finding you casually making yourself a drink.

“Drink?” you tilt your glass towards them.

“No, we don;t want a bloody drink. We want an explanation!” Yoonho stalks across the room before being halted by a hand on his shoulder.

“ What our hot-headed friend here meant to say was. Are you okay? What happened bak there? We're worried about you.” Jongins voice softened as he spoke to you. You felt suspiciously like he was talking to a scared cornered animal, one he wasn;t sure if it was going to run from him or fight.

“You know, you two spend an awful lot of time together and are very touchy feely for two people that are supposed to be rivals.” You try to lighten the mood and take the spotlight off yourself. At your words Jongin takes his hand off Yoonho's shoulder like it burned him. If you looked close enough your sure you could see the tell tale sign of red in Jongin cheeks as well,

“Don't go changing the subject.” You should have known it was not going to be that easy.

“I don’t know what to tell you.” you shrug

“Why don’t you start from the beginning. How do you know Hunter Sung?” Now you really were starting to feel like a cornered animal.

“That's not my story to tell, at least not mine alone.”

“But you said he doesn't remember you?” The anger is gone from Yoonhos voice, now the only thing to feel from him is sympathy.

“That's right. I don't know how and I don't know why. What I do know is that I am a firm believer of not starting a story I can't finish. Which means this is not a tale I can tell. Not yet anyway.

As Jinwoo watched his shadows fight the beasts he couldn’t help but be distracted. Thoughts of that mysterious woman plagued his mind. He couldn’t help but run over every memory he had trying to find her. To explain why she thinks they have met before. But nothing. He knew for certain he had not met her since becoming a player, which meant he must have met her when he was still known as the World's Weakest Hunter. But then what could he have possibly done to make her hate him, how could he have hurt her like that?

She was beautiful, funny and, to his surprise, powerful. Not quite as powerful as him but she could definitely give the other S-Ranks a run for their money. Who was she? She must be a hunter with power like that so why was she not at the raid of Jeju Island?

He had hoped to get some answers out of her at their last meeting but Jinwoo had been called away to deal with a gate that had opened and was causing chaos. The gate was in the upper levels of what would be considered A-Rank and all the other S-Ranks and their parties were either already busy or were too far away. Jinwoo had reluctantly left the cafe, assignment and shadow to his new obsession in the hopes of being able to catch her at her apartment later that day. Only the gate had turned red as soon as he stepped inside. At least he was still able to keep an eye on her through his connection with the shadow soldier, plus Beru would be able to protect her if needed. It was a risk assigning one of his strongest soldiers to keep an eye on her, but Jinwoo felt it was definitely worth it to keep her safe. The army would make do without one of its generals. Shortly after stepping through the gate he’d lost contact with Beru, Jinwoo tried not to panic, there was nothing he could do about it but he may have used excessive force on a few beasts. Besides Beru had not respawned with him so he hadn’t been killed. Jinwoo just couldn’t communicate with him. Where had the little minx gone that severed his connection to the shadows?

It had taken some time but soon the connection had been restored only for Jinwoo to see his girl fast asleep on the top of her bed, spread eagle in what appeared to be hunters gear. Jinwoo demanded answers from Beru, if bugs could look smug, that was the face Beru was giving Jinwoo. Beru refused to answer, knowing that Jinwoo would not call him away from his charge in order to punish him. Beru had decided that Jinwoo needed to find out what the minx was capable of by himself. Jinwoo wished he sent Igris instead.

Jinwoo had been in the red gate for a few days now, a constant feeling of melancholy washing over him from his connection to his girl. It had started on the first day, after some intense feelings of fear and then anger. She’d been sad ever since. Jinwoo really wanted to defeat this gate so he could go to her.

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@weaponxgames

@tanspostsblog

@bubera974

@nightmarewasteland

@o-qi-shisme

[argumate]

This is why, for all years of promising to boost consumption, it has been so hard for China to make much progress. It has to raise the household share of GDP by ten percentage points at the very least, which of course means an equivalent reduction of someone else's share.

Many analysts insist that China will choose to avoid rebalancing altogether, but they miss the point. These levels of imbalance simply cannot be sustained if neither China nor the rest of the world can absorb the growing gap between consumption and production.

China will rebalance one way or another. The important question is how it rebalances: whether an increase in the household share of GDP will occur in the form of a debt crisis and a sharp contraction in GDP, as occurred in the US in the early 1930s, or of many years of stable consumption growth and much lower GDP growth, as occurred in Japan after 1990, or of a surge in consumption that keeps GDP growth stable (which would be historically unprecedented). These are arithmetically the only three ways to rebalance.

[lyxthen]

I am a Marxist not in the sense that I think Marx (and Engels) were "right about everything" but in the sense that pretty much all social sciences today have their roots in Marxist thought, because he was the one to propose a more scientific approach to the study of society and social dynamics, focusing on material conditions and their impact, on the things that can be observed and measured and studied. Dialectical materialism and critical theory are to sociology what natural selection and gene theory are to biology.

Of course, it doesn't mean Marxism sacred, that there aren't things to revise or add or discard. We have to question these things if we want to make progress, the same way questioning the law of universal gravitation led to the discovery of relativity. This isn't a cult, it is not supposed to be, we are meant to debate and argue, because that's in the spirit of science. Infighting is not a bug, it's a feature.

The wider society needs to understand Marx not as an extremist political figure (which is what U.S. sponsored propaganda has turned him into, I believed this for a long time), but as a philosopher, the most important philosopher of modernity, in fact. We also need to teach history as a science, instead of as a collection of fables centered around specific individuals, with a clear narrative structure and a sweet little moral at the end to wrap it up. That is not how things work.

I remember, back when I was like 15, when I got my first Engels reading for school: The Part played by Labour in the Transition from Ape to Man. I rolled my eyes, because I'd heard from the right-wing political YouTubers that anything remotely associated with Communism was evil, and I was just starting to deconstruct all that, calling myself a centrist and all that. But instead of revolutionary propaganda, what I found was just... science. Science I already knew about, and that I knew was true. It's not a particularly challenging read, and while some ideas are outdated, the text has aged surprisingly well, over all.

I liked the essay. I really, really liked it. I still hold it dear to my heart, flaws and all, because it made me realize that maybe these radical leftists weren't so scary. If one of their most prominent thought leaders turned out to be a reasonable, approachable guy, maybe they were reasonable, approachable people, too.

So I kept reading, and I kept learning. It took me years to finally come to terms with the fact that every field from sociology to economics to psychology had been influenced or directly sprouted from Those Communist Guys, and even longer to finally admit that yes, I am a communist too, because instituting communism through violent revolution is the only reasonable response to the systems of exploitation behind poverty and climate change, and we should probably set things on fire about it.

(Meeting actually practicing communists helped a lot, too. Turns out, the guys committing acts of domestic terrorism against the local government are actually kinda chill.)

What I mean to say is this: we need to teach people how the world actually works first. We can radicalize them later, but the first step is giving them the tools to accurately describe and understand their reality. Not everyone has to become a scholar, I certainly am not, but getting familiar with the basics is essential, the same way it's essential to learn to read and write, and perform basic arithmetic. I was lucky enough that this was taught to me in school, and I can attest that it makes a difference.

We live in a world where misinformation and conspiracy theories on social media are turning our kids into little fascists. We need to bring them back to earth before it's too late.

[ryanhamiltonwalsh]

Walking by the court house in Dedham, MA the other night, I started thinking about Sacco & Vanzetti again, and their infamous, shameful trial in the same building where—despite a mountain of evidence and worldwide protests in their favor—they were found guilty and subsequently executed in 1927.

Woody Guthrie wrote an entire album about it, and if you've never heard the folk legend sing the town name Dedham ("we're stuck here in this dark Dedham jail"), you can remedy that here.

At the time, a Supreme Court justice owned a second home in Dedham, just a few yards away from the jail in question. Louis Brandeis, appointed by Woodrow Wilson, was a Supreme Court Justice of the United States from 1916 to 1939. A good summary of Brandeis, and why he was controversial, came from a fellow justice and went like this: "Brandeis was a militant crusader for social justice whoever his opponent might be. He was dangerous not only because of his brilliance, his arithmetic, his courage. He was dangerous because he was incorruptible … [and] the fears of the Establishment were greater because Brandeis was the first Jew to be named to the Court."

Brandeis adored Dedham, telling his brother, "Dedham is a spring of eternal youth for me. I feel newly made and ready to deny the existence of these gray hairs." I didn't know it until recently, but I walk by this house once a week on my hometown walk-route with my friend Julia. 195 Village Ave.

Louis Brandeis's wife, Alice Goldmark Brandeis, was perhaps even more progressive than her husband, well known as a vocal proponent of women's rights and labor causes. During the trial of Sacco & Vanzetti, she permitted Sacco's family to stay in their Dedham home to make visits to the jail easier. And get a kleenex ready, because one detail related to that you simply must know is: "Sacco's seven-year-old son, Dante, would sometimes stand on the sidewalk outside the jail and play catch with his father by throwing a ball over the wall." Additionally, Alice made a significant donation to their defense fund.

The entire case is fascinating, multi-faceted, full of twists and turns and potential evidence tampering by law enforcement, and in that way (and only that way), it is similar to what's being tried there right now. Officer Albert Hamilton tried to walk out of the court room with Sacco's gun, only to be stopped at the last moment by the judge. Post-trial, police Captain Van Amburgh took Sacco and Vanzetti's guns and bullets home, where they stayed until 1960 (!) until the Boston Globe uncovered the scandal. If you're curious, I recommend reading Tragedy in Dedham by Francis Russell.

They were found guilty. Worldwide protests erupted. Bombs were mailed. 20,000 gathered at Boston Common. Pleas for clemency abounded.

"Sacco and Vanzetti’s lawyers, rebuffed by the Supreme Judicial Court of Massachusetts, aimed at convincing a justice to issue a temporary stay of execution until the U.S. Supreme Court could fully review whether the two men had received a fair trial. ...Louis Brandeis, another progressive justice, recused himself from the case, because his wife, Alice, had made a significant donation to Sacco and Vanzetti’s defense fund." — SCOUTSblog

This is all to say, hey, how about that? Recusing yourself from an issue because of your wife's strong, public opinions on the matter? Justice Alito and Thomas wouldn't be worthy of cleaning Brandeis's toilet.

[kaywavy]

transforming soffits reorganizing keys formalizing immersion joints justifying kick extractors advising aggregates managing elbows recasting connectors achieving aluminum trowels officiating disks exhibiting absolute spigots progressing coil hydrants jerry-building reflectors informing casters inventing rubber hoists performing wrenches judging chalk adapters upgrading ignition paths

regrowing flashing recommending ratchets approving barriers sweeping impact fillers sewing mirrors detailing collectors enforcing measures distributing systems presenting plugs interwinding registers piloting ash diffusers gathering cranks supplying eave pockets undertaking scroll stops accelerating straps designing fittings protecting diamond boilers logging downspouts correlating shingles uniting mallets qualifying electrostatic lifts sharing clamps obtaining circular fluids ranking foundation gauges sensing miter brackets originating space networks translating drills regulating guards selecting gable padding utilizing pellet dowels reconciling artifacts altering pulleys shedding space filters determining vents representing mortar remaking flash rakers supporting funnels typecasting rotary chocks expressing junctures resetting auxiliary vises professing strip treads inlaying matter trowels questioning drivers forming edge fittings sketching blanks overshooting spark breakers rewriting controls playing tunnels inventorying buttons enduring joint handles effecting ratchet bibbs unwinding couplings forsaking vapor conduits defining sockets calculating heaters raising grids administering tiles measuring resources installing ignition remotes extracting corners manufacturing ventilators delegating consoles treating mounting stones enacting jig deflectors intensifying alleys improvising cargo pinpointing bobs prescribing arc masonry structuring metal chucks symbolizing lathes activating plumb kits adapting coatings fixing channels expediting cordage planning compressors enlisting hangers restructuring keyhole augers shearing ridge hardware collecting reciprocating bolts maintaining corrugated dimmers whetting hole collars conducting mandrels comparing assets compiling sealants completing paths composing equivocation wheels computing dampers conceiving electrostatic treatment ordering cotter grates organizing ties orienting ladders exceeding materials targeting thermocouples demonstrating emery stock expanding latch bases training wardrobe adhesives overcomming[sic] fasteners streamlining storm anchors navigating springs perfecting turnbuckles verifying gate pegs arbitrating arithmetic lifts negotiating outlets normalizing strips building surface foggers checking key torches knitting grinders mowing planers offsetting stencils acquiring bulbs adopting rivets observing avenues ascertaining coaxial grommets slinging wing winches instituting circuit generators instructing wicks integrating pry shutters interpreting immersion lumber clarifying coils classifying wood bits closing cogs cataloging matter strips charting holders conceptualizing push terminals stimulating supports overthrowing shaft spacers quick-freezing connectors unbinding ground hooks analyzing eyes anticipating gateways controlling proposition rollers converting power angles coordinating staples correcting benders counseling joist gaskets recording gutter pipes recruiting drains rehabilitating rafter tubes reinforcing washers reporting guard valves naming freize sprues nominating rings noting straps doubling nailers drafting circuit hoses dramatizing flanges splitting framing compounds refitting stems interweaving patch unions placing sillcocks sorting slot threads securing mode cutters diverting catharsis plates procuring load thresholds transferring syllogism twine directing switch nuts referring time spools diagnosing knobs discovering locks dispensing hinges displaying hasps resending arc binders retreading grooves retrofitting aesthetics portals seeking stocks shrinking wormholes assembling blocks assessing divers attaining lug boxes auditing nescience passages conserving strikes constructing braces contracting saw catches serving installation irons recognizing fluxes consolidating fuse calipers mapping shims reviewing chop groovers scheduling lag drives simplifying hoists engineering levels enhancing tack hollows establishing finishing blocks

[mariacallous]

In late 2017, Ashwin Sah and Mehtaab Sawhney met as undergraduates at the Massachusetts Institute of Technology. Since then, the pair have written a mind-boggling 57 math proofs together, many of them profound advances in various fields.

In February, Sah and Sawhney announced yet another joint accomplishment. With James Leng, a graduate student at UCLA, they obtained a long-sought improvement on an estimate of how big sets of integers can get before they must contain sequences of evenly spaced numbers, like {9, 19, 29, 39, 49} or {30, 60, 90, 120}. The proof joins a long line of work on the mathematical impossibility of complete disorder. It also marks the first progress in decades on one of the biggest unsolved problems in the field of combinatorics.

“It’s phenomenally impressive that they managed to do this,” said Ben Green, a mathematician at the University of Oxford. At the time the work was released, the trio were all still in graduate school.

Sequences of regularly spaced numbers are called arithmetic progressions. Though they’re simple patterns, they hide astounding mathematical complexity. And they’re difficult, often impossible, to avoid, no matter how hard you might try.

In 1936, the mathematicians Paul Erdős and Pál Turán conjectured that if a set consists of a nonzero fraction of the whole numbers—even if it’s just 0.00000001 percent—then it must contain arbitrarily long arithmetic progressions. The only sets that can avoid arithmetic progressions are those that comprise a “negligible” portion of the whole numbers. For example, the set {2, 4, 8, 16, …}, in which each number doubles the one before it, is so spread out along the number line that it’s said to make up 0 percent of the whole numbers. This set has no progressions.

Forty years later, in 1975, a mathematician named Endre Szemerédi proved the conjecture. His work spawned multiple lines of research that mathematicians are still exploring today. “Many of the ideas from his proof grew into worlds of their own,” said Yufei Zhao, Sah and Sawhney’s doctoral adviser at MIT.

Mathematicians have built on Szemerédi’s result in the context of finite sets of numbers. In this case, you start with a limited pool—every integer between 1 and some number N. What’s the largest fraction of the starting pool you can use in your set before you inevitably include a forbidden progression? And how does that fraction change as N changes?

For example, let N be 20. How many of these 20 numbers can you write down while still avoiding progressions that are, say, five or more numbers long? The answer, it turns out, is 16—80 percent of the starting pool.

Now let N be 1,000,000. If you use 80 percent of this new pool, you’re looking at sets that contain 800,000 numbers. It’s impossible for such large sets to avoid five-term progressions. You’ll have to use a smaller fraction of the pool.

Szemerédi was the first to prove that this fraction must shrink to zero as N grows. Since then, mathematicians have tried to quantify exactly how quickly that happens. Last year, breakthrough work by two computer scientists nearly solved this question for three-term progressions, like {6, 11, 16}.

But when you’re instead trying to avoid arithmetic progressions with four or more terms, the problem becomes tougher. “The thing I love about this problem is it just sounds so innocent, and it’s not. It really bites,” Sawhney said.

That’s because longer progressions reflect an underlying structure that is difficult for classical mathematical techniques to uncover. The numbers x, y and z in a three-term arithmetic progression always satisfy the simple equation x – 2y + z = 0. (Take the progression {10, 20, 30}, for instance: 10 – 2(20) + 30 = 0.) It’s relatively easy to prove whether or not a set contains numbers that satisfy this kind of condition. But the numbers in a four-term progression have to additionally satisfy the more complicated equation x2 – 3y2 + 3z2 – w2 = 0. Progressions with five or more terms must satisfy equations that are even more elaborate. This means that sets containing such progressions exhibit subtler patterns. It’s harder for mathematicians to show whether such patterns exist.

In the late 1990s, Timothy Gowers, a mathematician now at the Collège de France, developed a theory to overcome this obstacle. He was later awarded the Fields Medal, math’s highest honor, in part for that work. In 2001, he applied his techniques to Szemerédi’s theorem, proving a better bound on the size of the largest sets that avoid arithmetic progressions of any given length. While mathematicians used Gowers’ framework to tackle other problems over the next two decades, his 2001 record remained steadfast.

In 2022, Leng—then in his second year of graduate school at UCLA—set out to understand Gowers’ theory. He didn’t have Szemerédi’s theorem in mind; rather, he hoped to answer a technical question related to the techniques Gowers had developed. Other mathematicians, fearing that the effort needed to solve the problem would eclipse the result, tried to dissuade him. “For good reason,” Leng later said.

For more than a year, he didn’t get anywhere. But eventually, he started making progress. Sah and Sawhney, who had been thinking about related questions, learned about his work. They were intrigued. “I was amazed it’s even possible to think like this,” Sawhney said.

They realized that Leng’s research might help them make further progress on Szemerédi’s theorem. Within a few months, the three young mathematicians figured out how to get a better upper bound on the size of sets with no five-term progressions. They then extended their work to progressions of any length, marking the first advance on the problem in the 23 years since Gowers’ proof. Gowers had shown that, as your starting pool of numbers gets bigger, the progression-avoiding sets you can make get relatively smaller at a certain rate. Leng, Sah and Sawhney proved that this happens at a rate that’s exponentially faster.

“It’s a huge achievement,” Zhao said. “This is the kind of problem that I really would not suggest to any student because it is so incredibly hard.”

Mathematicians are even more excited by the method the trio used to get their new bound. For everything to work, they first had to strengthen an older, more technical result by Green, Terence Tao of UCLA and Tamar Ziegler of Hebrew University. Mathematicians feel that this result—a sort of elaboration of Gowers’ theory—can be improved even further. “It feels like we have an imperfect understanding of the theory,” Green said. “We’re just seeing a few shadows of it.”

Since completing the proof in February, Sah and Sawhney have both graduated. But the pair’s collaboration has not yet slowed down. “Their incredible strength is taking something that is extremely technically demanding and understanding it and improving upon it,” said Zhao. “It’s difficult to overstate the level of their overall accomplishments.”

[nimblermortal]

Sivagami is obviously very popular as a regent, she does a very good job ruling. Nobody wants a queen, obviously women are unfit to rule, but they would happily welcome another twenty years of Sivagami's regency while she raises up a new king. And another twenty after that, if that's what it took!

(They also really enjoy celebrating the child princes' birthdays, it's a whole thing.)

So what about her political policies?

Headcanon: She's set up a farmer-soldier caste where if you serve in the army for X years you get a plot of Y acres to farm, and it's not that she's been driving X down to spread wealth equality through the country, it's just that a lot of that military service is dressing in a uniform and holding the ceremonial spear and as long as you know the right rituals you don't actually have to fight and…

The army has never been larger! Most of the soldiers are completely incompetent at anything but comparing remedies for the maladies of sheep, and looking pretty

And this is why they have so many freaking soldiers on parade every time there's a big national event.

(Neighboring countries have pageants about why Sivagami has so very many pretty pretty soldiers)

Meanwhile Sivagami is all, "No one wants to spend money on economic restructuring with dubious promise of return on investment, but everybody wants to support our troops. Nobody wants to talk about cattle husbandry and sharing irrigation techniques that worked in Region 1 with Region 2, but neither will anyone question my deploying the 85th cavalry and the 101st infantry together to the region stricken by drought."

She demands that every soldier be able to read the orders she sends to them, she refuses to let her word be misinterpreted. She designs drills for her six-year-old sons to watch with military units as the beads on the abacus. This is for the military and mathematical education of her sons, obviously, not to teach the soldiers basic arithmetic. The five-year-service-gift of an abacus is a joke.

Some units get assigned to guard trade caravans, and learn about trade routes, foreign customs, how merchant routes work, and how to sell their military service farms back to the crown for the liquid assets to start their own firm.

Those who come to the army with no skills will obviously have to be put to things like tending horses, learning to shoe them, make tack... yeah, she's turned the army into a trade school for young men, which in turn reduces incidences of domestic violence and increases the wealth and comfort of the women of the country.

She has not figured out how to stop using the army for everything, and in another world she's super offended when Devasena sets up something similar for the women because women are supposed to be mothers! look after the houses!

Devasena might try to point to Sivagami's rotating caste of ladies-in-waiting, who all leave much, much more prepared for life than they arrived, but Sivagami hates the lot of them. She's offended by incompetence and demands a lot of education and progression in her ladies-in-waiting, who uh. Usually peel off to find a less demanding job, with all of their impressive batteries of skills. Which is why Sivagami doesn't have a ninja corps at the palace, and she's huffy about it.

If these women had any AMBITION, or if they would stick around long enough for her to find them suitable husbands, but noooooo they're off running the guild of goldsmiths and whatnot, the LAYABOUTS

[so-true-overdue]

The Gospel of Immunity: A Sermon on the Sacred Shield of Vaccination

Behold, the paradox of human cognition: we champion progress, yet tremble before its fruits.

In a world spinning upon the axis of relentless biological warfare—our cells besieged by microbial marauders—vaccines stand as sentinels, the silent paladins of immunological defense. Yet, their divine efficacy is often questioned by those who worship at the altar of anecdote, forsaking the empirical cathedral of science.

Consider the Magnitude of Their Grace

Vaccines are not mere concoctions of modern alchemy. They are the crystallized wisdom of centuries, born of Pasteur’s tenacity, Jenner’s courage, and the accumulated trials of countless minds wielding microscopes like swords. They have subdued polio’s paralysis, exorcised smallpox’s specter, and shielded countless millions from the venoms of measles, tetanus, and pertussis.

And what of their adversaries? The infinitesimal specter of adverse reactions. Let us quantify the peril: the risk of a severe allergic reaction to a vaccine—a dreaded anaphylaxis—is approximately one in a million. To contextualize, the chance of being struck by lightning in one’s lifetime is 1 in 15,300. Shall we eschew umbrellas next? Or perhaps condemn electricity itself as too great a hazard to endure?

On Negotiation with Risk

Vaccination is not the obliteration of risk; it is a calculated negotiation with uncertainty. To vaccinate is to weigh the scales of harm and benefit, to face the specter of a one-in-a-million reaction and declare that the lives of millions are worth that gamble. Contrast this with the toll exacted by diseases unopposed: measles alone claims the lives of over 100,000 annually, most of them children. This is not conjecture—it is arithmetic, immutable and unyielding.

Shall we refuse the shield because it may chafe? Shall we spurn the ship because it cannot promise calm seas? Such is the folly of those who elevate potential discomfort above the preservation of collective health. They barter statistical insignificance for certainty of peril, trading herd immunity for herd vulnerability.

The Poetry of Immune Memory

The true marvel of vaccination is not merely its prevention but its pedagogy. Vaccines instruct our immune system, training it to recognize the invader before the battle has begun. They are rehearsals for wars that may never come. To vaccinate is to inscribe within the body a symphony of defense, a living testament to humanity’s ingenuity and resilience.

Without this foresight, the immune system becomes a tactician unprepared for the ambush. Disease ravages unchecked, leaving scars upon both flesh and society. Vaccines, therefore, are not just medicinal; they are ethical. They embody the moral imperative to protect not only oneself but the vulnerable—the infant, the immunocompromised, the elder.

A Closing Admonition

Let us not falter in the face of misinformation, for it spreads with a virulence rivaling the diseases we seek to defeat. Let us arm ourselves with knowledge and statistics, with reason and compassion. The act of vaccination is an act of faith—not blind faith, but faith rooted in evidence, nurtured by science, and borne aloft by the unassailable truth that humanity is stronger united.

Go forth, then, and spread the gospel of immunity. For in the armory of progress, the needle is mightier than the microbe.

[jokertrap-ran]

[スタオケ] La Corda d'Oro Starlight Orchestra Osakabe Seiji Cast Story Chapter 3 Translation

*Starlight Orchestra Masterlist | Osakabe Seiji’s Personal Masterlist *Spoiler free: Translations will remain under cut *Osakabe’s Route Tag will be #Seiji’s Star

Sakuya: Wrong. This should be solved using a geometric progression formula, not an arithmetic progression formula.

Sakuya: *Sigh* …This is impossible. It may just be a small test, but there's no way you can cram for it the night before.

Sakuya: You’ll have supplementary classes lined up in your foreseeable future if you fail to get at least 60 marks. Are you even aware of that?

Sakuya: You look appalled… Is this your first time hearing about this? Looks like you weren't listening to what the teacher said at all.

Sakuya: Though, it looks like this is the price you'll have to pay for only focusing on practice and sleeping through all your classes. Good luck.

Sakuya: There's nothing I can do to help you here. See you.

I just got abandoned…

Seiji: Why, if it isn't the Concertmistress?

Seiji: What a face you're making. Look at those dead eyes of yours.

Seiji: Are you studying for a test? I could hear your conversation with Kujo out in the hallway.

Seiji: Isn't a quiz just to check how much you've learned in class? You should be fine if you understood whatever they were teaching in class. 

Seiji: I think it's much harder to rush and try to cram everything in one day on the day before the test.

Seiji: Well, do your best. Studying is something best done in solitude.

Seiji: …What's wrong? Why are you grabbing the hem of my shirt?

Seiji: You must be in a rather dire situation if you're clinging to me like that so desperately.

Seiji: Hmph… I'm no demon either.

Seiji: If you ask nicely enough, perhaps I'd feel more inclined to be your personal tutor tonight.

Seiji: —Now, what will you do?

☆ ━━━━━━━ ∘◦♬◦∘ ━━━━━━━ ☆

My brain was overwhelmed by the large amount of formulas that had been rapidly crammed in…

Seiji: …Hey.

Seiji: Have you fallen asleep with your eyes open? Your hand stopped moving.

Seiji: My, my, it wouldn't do for you to be stuck and wasting time on such a simple question.

▷Choice: Sorry, Sir. My brain can't take it anymore…

Seiji: Oh dear, are you giving up here? It appears that I may have been a little too strict. Seiji: And here I thought that perhaps you'd be able to take it.

▷Choice: I can only cry…

Seiji: What I want is a solution, not tears. Seiji: Well, since it doesn't look like your brain’s functioning anymore, it'll be useless to attempt cramming anymore.

Seiji: How unfortunate.

Seiji: I was planning on treating you to a fruit parfait next Saturday for all the hard work you've done.

Seiji: One from a high-end fruit parlor, priced at over 2,000 yen.

Seiji: Not to mention, lavishly decorated with various shiny and jewel-light fruits… I dare say it must be very fresh and delicious.

Seiji: I suppose that would have to be put on hold if you're just going to give up here.

▷Choice: I'll do my best!!!

Seiji: Brilliant. Seiji: Although, hard work alone is not enough. Even a monkey can do it, you see. Seiji: You'll have to pass the test first if you want to get your hands on the parfait, no? Seiji: Kujo told you, didn't he? About how you're going to have to take supplementary classes if you fail.

Seiji: I'm sure it wouldn't be a good look for us if word gets out that the Concertmistress of the Starlight Orchestra is undergoing remedial.

Seiji: So do your best to pass. Understood?

☆ ━━━━━━━ ∘◦♬Seiji’s Star♬◦∘ ━━━━━━━ ☆

Previous Part: (Chapter 2) Next Part: (Chapter 4)

[snarkythewoecrow]

(warning one giant run-on sentence about my childhood ahead)

eating soup and the most random memory from childhood popped into my head, and tbh, i don't exactly remember how old i was, but it involved some experiences in 2nd and 3rd grade

back then, in the 80s, they didn't have real supports for kids that were struggling, and in our town, they tended to just label some kids as unteachable and pass them upwards through the grades cuz they weren't reading or writing or doing whatever else little gremlins should be doing--and when it came to me? i couldn't read, so obviously wasn't writing, and pretty much not talking either

so yeah, i was one of those kiddos they labeled, and it wasn't until the summer between second and third that a very nice teacher cared enough to say something about it, she didn't treat me like i was stupid, but always looked at me more like i was a little puzzle to be worked out,

and the commitment of this woman, bless her cuz looking back i can see how hard she went to help, because let me tell you, my mother? a total cunt, and this woman befriended her, inserted herself into our lives over that summer, maybe under the guise of getting into my mother's little social circle, but like i said, looking back, i can't say i ever remember her giving two fucks about my mother or her shitty lunches, this teacher spent time working with me

and it was that summer, between the 2nd and 3rd grade, that i didn't so much make a slow progression to reading, but rather, i decided she seemed pretty fucking nice and so yeah, i could do that for her

so yeah, i went from not reading in the 2nd to devouring the written word in the third, which was the year i sat in the corner of the school library reading this worn hardcover copy of the devil's arithmetic, which started me on a path of questioning and thinking that i never would have otherwise

it's crazy what a little kindness and patience one summer did for me, and on a less serious note, or maybe the most important one, it's because of Mrs Norwood that you've all been graced with my kinky, smutty fics, we all owe her a big thank you

[nablah]

Lessons from the Changing Times: Towards a Relevant View and Practice of Science and Technology in Society

Lesson 1: The Coupling of Knowledge and Science and Its Impacts in the Human Society

As an aspiring scientist, I believe that the concept of unquestionable scientific truth contradicts science. The scientific method reveals that by “observing, asking questions, and seeking answers through tests and experiments”, science depends on the unique experience of individual humans and their interactions with the world. This standard, which resulted from colonial and imperial powers integrating knowledge systems in colonies to conform to an idea of “civilized” methodology and knowledge1, also begs the question of what we consider the authority on truth: is it science or how colonizers performed science? This subjectively informed method supposedly yields objective truth– but how true is this?

Heisenberg’s uncertainty principle from physics, Gödel's incompleteness theorem, and Tarski's undefinability theorem from mathematics (applied to the simplest systems of space, time, arithmetic, and mathematical logic) [2][3], all impose limitations on the observation and provability of phenomena to certain degrees of accuracy. If the scientific method admits uncertainty of the most fundamental "truths", then science does not yield “truth” but verisimilitude. Arguably, history, psychology, art, music, and other disciplines have their own verisimilar “truths". Like how different colors constitute white light, only a combination of these verisimilar truths can reveal a clearer picture of the world.

Lesson 2: Science and Technology (S/T) as Social Forces

As humans, scientists study what interests them and interpret the world according to paradigms: worldviews that tell them how to think and act. The German chemist Kekulé theorized benzene as having a cyclical structure after dreaming of an ouroboros4. This was eventually validated, making significant progress in benzene’s industrial applications. Despite what scientism and techno-progressivism claim, the scientist and their craft, as with all humans and human endeavors, are influenced by society and politics; claiming that one may act without responsibility towards fellow humans is itself a sociopolitical statement. Science, while striving to reach a value-free ideal, is nevertheless a value-laden discipline. 

As a child, I was drawn to the idea of a scientist “doing only the best for humankind”. Today, I ask: “Who determines what is best for humankind?” Decades after Kekulé, benzene was used in Nazi Germany to execute prisoners through lethal injection. Under science’s colonial legacy and consequent authority, scientists as sociopolitical figures have, ironically, seldom, if any, control over the sociopolitical effects of their work, as benzene has shown. Thus, seeing science as a sociopolitical force that acts throughout history helps us question and develop safeguards against misusing science and technology’s elevated status in society.

Lesson 3: Science, Technology, and Society as Optics of and Tool for the New Normal

History is littered with examples like benzene. Time and again, science and technology act as revolutionary forces, pushing paradigm shifts in economic, industrial, and political spheres. Beyond acting as sociopolitical forces, science and technology also move as socioeconomic forces, driving and being driven by economic development. From the first industrial revolution (IR) to the fourth, the supremacy accorded to science by colonial and imperial structures persists in the capitalistic emphasis on what we produce and how good we are at producing it [5]. Essentially, science itself has become a commodity to buy, sell, and ultimately, control through its perceived value in advancing societies.

Society stepping forward is inevitable; however, from the example of previous IRs and the growing global consciousness resulting from IRs, we must not tread on anyone in the process. The first IR mechanized production but also popularized slave labor and worsened the living conditions of the working class. The second IR engaged in mass production and consumerism. The third IR produces cheaper, more efficient electronics, but condemns Congolese citizens to violence and genocide with increasing demand for materials. Looking at what the next revolution will bring, we must first question what it seeks to accomplish and for whom.

Lesson 4: Competition / Cooperation as Drivers of S/T

Revolutions like the fourth IR show what they seek and for whom in competition and cooperation behaviors between actors within and outside science and technology. With the spread of globalization, communication between participants has allowed international, diverse perspectives on the development of science and technology, especially in the context of the digital age. However, the loudest voices constitute the main dialogue in international conversations toward equitable economic progress. Core nation-states (e.g., the US, UK, China, Russia), historically colonizing empires, dominate periphery nation-states in labor and capital [6]. While some periphery nations like Singapore can eventually progress alongside core nations, the growing disparity between the two nation types ensures that only cooperation with the core ensures the survival of the periphery state– a reinforcement of the core nations’ status. 

This behavior is reflected in firms and industries, where cooperation and competition’s end goal is to gain a competitive advantage over their rivals. Strategic alliances are made, but who benefits at minimal compromise? Like how Apple and Microsoft cooperated, these strategies influence and are influenced by the benefits, pace, and priorities of the initial dominating entity– this is merely a smaller replication of the inequitable systems in the world today.

Lesson 5: Social Dynamics Set in Motion by New Technology

We have seen how science, like any other study of the world, seeks to discover truths about our surroundings. The current state of science and technology seeks to uphold the status quo in society, politics, and economics as established in the past by colonial and imperial actors. Given that, how should science proceed, knowing that science must still progress when all is said and done?

We have a saying in radiation physics: rules are written in blood [7]. It’s an acknowledgment of the lives lost when dealing with something we don’t know– an unfortunate, sometimes necessary collateral in the name of scientific progress. For science to progress, we must acknowledge the past sacrifices given (and taken) in discovery’s name. Acknowledgment means full responsibility and includes educating people about history alongside scientific concepts. We must answer the question of whose blood was spilled and why their blood was necessary to discover those rules. Second, if science’s future (it cannot be irredeemable) is for the good of humanity and ameliorating systems in our world, then science must stop working for forces against humanity and the betterment of the human condition. The cycle of unjustly shedding blood for progress must stop.

Lesson 6: Filipinos in Science and Technology

We’ve discussed how personal politics do not necessarily translate to the politics of science and technology. However, scientists and technology workers who love and believe in the potential of their fields to help people understand their world and make it better still exist. From the lives and works of Filipino scientists, the global struggle of scientists and science workers continues, that of the fight for decolonial, equitable, and accessible science and technology, where no one is left behind. 

We see this in how Leonard Co and Edgardo Gomez shared the struggle of indigenous people for autonomy and their efforts to document and preserve indigenous knowledge and our environment, how doctors Fe del Mundo and Juan Salcedo innovated medicine and nutrition to address socioeconomic struggles in Philippine healthcare, and how Julian Banzon and Maria Orosa utilized local materials in food and energy, contributing towards our economic independence– I only hope to emulate them. I am, as of the moment of writing, grief upon grief, mourning the physical and epistemological deaths of scientists from colonialism and imperialism [8][9][10] but I also hope against hope that science and technology will have a future in society, one that acknowledges, learns, and grows from its past.

References:

[1] Said, E. W. (1978). Orientalism (pp. 62–68). Penguin.

[2] Calude, C. S., & Stay, M. (2007). From Heisenberg to Gödel via Chaitin. International Journal of Theoretical Physics, 46(8), 2013–2025. https://doi.org/10.1007/s10773-006-9296-8

[3] Woleński, J. (2005). Godel, Tarski and Truth. Revue internationale de philosophie.

[4] Read, J. (1995). From alchemy to chemistry (p. 179). Dover.

[5] Marcuse, H. (1964). One-dimensional man  studies in the ideology of advanced industrial society. Routledge.

[6] Wallerstein, I. (1989). The modern world-system. Academic Press.

[7] Osborne, S. (2023). Rules written in blood: A case study of risk management in the oil and gas industry. Delhi Business Review, 24(1), 1–16. https://doi.org/10.51768/dbr.v24i1.241202301

[8] Sawafta, A., Tolba, A., & Makary, A. (2023, December 3). Israeli air strike in Gaza kills prominent scientist Sufyan Tayeh, Palestinian ministry says. Reuters. https://www.reuters.com/world/middle-east/israeli-air-strike-gaza-kills-prominent-scientist-sufyan-tayeh-palestinian-2023-12-02/

[9] Niarchos, N. (2021, May 24). The Dark Side of Congo’s Cobalt Rush. The New Yorker; The New Yorker. https://www.newyorker.com/magazine/2021/05/31/the-dark-side-of-congos-cobalt-rush

[10] Glenn, M. (2023, October 11). Israel strikes university in Gaza it said was training Hamas fighters. The Washington Times. https://www.washingtontimes.com/news/2023/oct/11/israel-strikes-university-gaza-it-said-was-trainin/

[edugamingappworld]

Maths Games For Kids: Make Learning Numbers a Joyful Journey

Mathematics often conjures images of textbooks, repetition, and complexity—but it doesn’t have to. In the digital era, children no longer have to fear numbers or formulas. Thanks to intuitive and playful technology, Maths Games For Kids have revolutionized how young minds absorb numerical knowledge. These games fuse learning and entertainment into a single, irresistible experience.

At EduGaming App World, we understand that early exposure to math must be engaging, not intimidating. Our collection of Maths Games For Kids is designed to empower young learners through challenge, creativity, and fun.

🎯 Why Are Maths Games Important for Children?

Children are naturally curious. They thrive in environments that challenge their imagination and allow active participation. Math, however, often gets a bad reputation for being abstract and “boring.” That's where Maths Games For Kids step in.

These games:

Build foundational arithmetic skills (addition, subtraction, multiplication, division)

Improve problem-solving and critical thinking

Strengthen memory and cognitive flexibility

Encourage independent learning and resilience through gamified reward systems

When children play math games, they're not just memorizing—they're exploring, experimenting, and developing a lasting relationship with numbers.

🧠 What Makes a Good Maths Game?

Not all math games are created equal. At EduGaming App World, we curate games based on the following educational principles:

Age Appropriateness Games should be tailored to developmental stages—from number recognition in preschoolers to fractions and geometry in elementary learners.

Interactive and Adaptive Design Games must adapt to a child’s performance, offering increased challenges as they progress.

Visual and Auditory Engagement Sounds, animations, and colorful characters create a multisensory learning experience that keeps kids coming back.

Curriculum Alignment The best Maths Games For Kids reinforce what children are already learning in school.

Safe and Ad-Free Environment We ensure a secure, child-friendly platform where learning is never interrupted by intrusive content.

🕹️ Popular Types of Maths Games

Our platform hosts a wide variety of math games. Here are some of the most loved by kids and approved by educators:

1. Counting Games

Perfect for toddlers and preschoolers, these games teach basic number recognition and counting through visual objects, animals, or characters.

Example: Count the stars in the night sky or feed a monster the right number of cookies.

2. Addition & Subtraction Challenges

These games make simple arithmetic fun by using visual puzzles, flashcards, or time-bound challenges.

Example: Help a frog jump from lily pad to lily pad by solving addition problems.

3. Multiplication Races

Kids compete in virtual races where each correct multiplication answer powers their vehicle forward.

Example: Rocket Math—solve x-table questions to blast off faster than your opponents.

4. Math Puzzles & Mazes

Mazes and brain teasers where kids solve math questions to move forward or unlock levels.

Example: Solve equations to escape a pirate’s treasure cave.

5. Shape and Pattern Recognition

Early geometry games that help children identify basic 2D and 3D shapes, symmetry, and patterns.

Example: Match shapes to build a robot or replicate patterns to create a pixel art picture.

📱 Why Choose EduGaming App World?

There are countless platforms offering Maths Games For Kids, but here's why EduGaming App World stands out:

Feature

Benefit

Age-based game categorization

Kids play games aligned to their skill level

Progress tracking

Parents and teachers monitor improvement

Daily rewards & streaks

Motivation through achievement badges and levels

Offline play mode

Accessible even without internet connection

Zero ads & data safety

100% child-safe gaming environment

Whether your child is a math whiz or a hesitant beginner, our games foster self-paced growth in a pressure-free atmosphere.

👪 Who Can Benefit from These Games?

Parents: Looking for screen time that educates as it entertains

Teachers: Wanting digital tools for classroom reinforcement

Homeschoolers: Needing curriculum-supportive content

Kids (aged 3 to 10+): Craving interactive adventures, not boring worksheets

💡 Tips to Maximize Learning with Maths Games

To get the most out of your child’s math gaming experience, follow these simple tips:

Set daily or weekly game time goals (15–30 mins works best)

Play alongside your child occasionally to encourage discussion

Use in-app progress reports to see where your child excels or needs support

Celebrate milestones—badges, streaks, or level-ups can be great motivators

🎓 Aligning with School Curriculum

Our Maths Games For Kids are carefully mapped to early childhood learning standards and Common Core principles. Whether your child is learning number lines, time, money, or decimals, our platform supports those lessons through digital reinforcement.

Teachers using our platform also gain access to:

Lesson planning tools

Assignment tracking

Collaborative classroom competitions

🚀 Final Thoughts: Turn Math Fear into Math Fun

The best way to nurture a child’s love for math is by connecting it to joy and exploration. With the right tools, what once felt like a burden can become a favorite activity.

EduGaming App World is committed to transforming traditional learning through interactive, purposeful gaming. Our collection of Maths Games For Kids blends fun with focus, guiding young learners toward mastery—one cheerful click at a time.

Original Source  : https://edugamingappworld.com/maths-games-for-kids/

[chhibrin]

How to Crack CDS in First Attempt – A Complete Guide by IFA Defence Academy

Cracking the Combined Defence Services (CDS) exam in the very first attempt is a dream for many young aspirants who want to serve the nation with pride and honor. The exam, conducted by the Union Public Service Commission (UPSC) twice a year, is highly competitive and demands a well-planned strategy, consistent effort, and the right guidance.

In this comprehensive blog post, we at IFA Defence Academy — a leading name for CDS coaching in Chandigarh — will walk you through a detailed roadmap to clear the CDS exam in your first attempt. Whether you're still in college or have just graduated, these tips will set you on the right track.

Understanding the CDS Exam Structure

Before diving into preparation strategies, it is crucial to understand the exam pattern:

For IMA, INA, and AFA:

English – 100 Marks

General Knowledge – 100 Marks

Elementary Mathematics – 100 Marks

For OTA (Officers’ Training Academy):

English – 100 Marks

General Knowledge – 100 Marks

All papers are objective type with a negative marking of 1/3rd for every wrong answer. Understanding this structure helps tailor your preparation accordingly.

Step 1: Make a Realistic Study Plan

Planning is the first step to success in any competitive exam.

Divide your syllabus: Break the topics into daily or weekly goals.

Set achievable targets: Don't overburden yourself. Instead, focus on consistency.

Mix subjects daily: Instead of studying one subject per day, study 2–3 subjects to avoid monotony.

At IFA Defence Academy, our faculty helps students create personalized study plans which is one of the reasons we're trusted for CDS coaching in Chandigarh.

Step 2: Strengthen the Basics

A common mistake many aspirants make is jumping directly to mock tests and shortcuts. Start by building strong conceptual clarity, especially in:

English Grammar & Vocabulary

Current Affairs & Static GK

Fundamentals of Arithmetic, Algebra, Trigonometry, and Geometry

Books like NCERTs (Classes 6 to 10 for Maths) and Lucent for GK are great to begin with. For English, Wren & Martin and newspaper editorials can be excellent resources.

Step 3: Practice Previous Year Papers

One of the most effective strategies is to analyze and solve previous year papers:

Understand question patterns and difficulty levels.

Identify frequently asked topics.

Practice time management during exam conditions.

IFA Defence Academy provides a repository of solved previous year papers as part of its comprehensive study package — an added advantage of enrolling in the best CDS coaching in Chandigarh.

Step 4: Take Regular Mock Tests

No preparation is complete without evaluating your progress. Enroll in a well-structured test series that mimics the actual exam.

Attempt at least one full-length test weekly.

Analyze your performance after every test.

Work on weak areas before the next test.

Mock tests improve speed, accuracy, and time management — key elements in clearing the CDS exam on your first try.

Step 5: Focus on Physical Fitness for SSB

Cracking the written exam is only half the battle. The SSB Interview is equally crucial and includes psychological tests, group discussions, physical tasks, and personal interviews.

IFA Defence Academy emphasizes complete training, including SSB interview preparation, group tasks, and personality development, making it a preferred choice for CDS coaching in Chandigarh.

Tips for physical readiness:

Jogging or running daily

Building upper body strength

Practicing group activities and leadership exercises

Step 6: Stay Updated with Current Affairs

The General Knowledge section can be a game-changer. To score well:

Read newspapers like The Hindu or Indian Express daily.

Watch news analysis on channels like Rajya Sabha TV.

Prepare monthly current affairs notes (or follow a reliable monthly magazine).

IFA Defence Academy provides daily and weekly GK capsules tailored specifically for CDS aspirants.

Step 7: Maintain a Positive Mindset

Staying confident and mentally strong is as important as academic preparation.

Avoid burnout — take regular breaks.

Stay motivated by reading biographies of defence personnel.

Surround yourself with like-minded aspirants.

At IFA Defence Academy, we believe that mentorship, peer interaction, and a disciplined environment are key to transforming potential into performance.

Why Choose IFA Defence Academy for CDS Coaching in Chandigarh?

Here’s why hundreds of students trust us every year:

Experienced Faculty: Retired defence officers and UPSC experts.

Updated Study Material: Designed as per the latest exam trends.

Personalized Mentorship: One-on-one guidance for each student.

Regular Doubt Sessions & Tests: To keep progress in check.

SSB Interview Preparation: Integrated into the coaching program.

If you're serious about your CDS journey, joining a reliable institute like IFA Defence Academy for CDS coaching in Chandigarh gives you a strategic edge.

Final Thoughts

Cracking the CDS exam in your first attempt is entirely possible if you have:

A clear strategy

Strong fundamentals

Dedicated practice

Right guidance

IFA Defence Academy is here to support you at every step of this journey. If you’re looking for the most trusted and results-driven CDS coaching in Chandigarh, your search ends with us.

Start early, stay focused, and success will follow.

Ready to start your journey toward a career in the Armed Forces?

Get in touch with IFA Defence Academy today — your first step toward wearing the uniform with pride.

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