#Arithmetic

[nemfrog]

Cat threesomes.

Seeing Through Arithmetic - 3. 1955.

Internet Archive

[from-a-spiders-web]

Laurent de La Hyre | Allegory of Arithmetic (detail) 1650

[blondebrainpowered]

Watercolour portrait of Ada King, Countess of Lovelace also known as Ada Lovelace, ca. 1840, possibly by Alfred Edward Chalon.

Ada Lovelace, is celebrated as the first computer programmer. In the early 19th century, she wrote detailed notes on Charles Babbage’s Analytical Engine, a pioneering mechanical computer.

Among these notes was an algorithm designed to compute Bernoulli numbers, which is recognized as the first published computer program. At a time when computing was an uncharted territory, Lovelace envisioned the potential of machines to perform complex tasks beyond basic arithmetic.

Her foresight and contributions laid the groundwork for modern computer science.

She was also the daughter of the poet Lord Byron.

[noosphe-re]

The monad is like a seed in containing in itself the unformed and also unarticulated principle of every number; the dyad is a small advance towards number, but is not number outright because it is like a source; but the triad causes the potential of the monad to advance into actuality and extension. 'This' belongs to the monad, 'either' to the dyad, and 'each' and 'every' to the triad.

Iamblichus, The Theology of Arithmetic, translated by Robin Waterfield

[graementality]

Mind's third - ARITHMETIC

Arithmetic from @paleduck0000 ( @cccc-enata-au )'s Énata AU!!

Some alt versions below the cut :]

(click for better quality bcus tumblrs a bitch)

Without his crown + the original line art before I decided to make this line-less bcus why not!

[wahroh]

Numerically speaking of course.

[demifiendrsa]

Vanillaware 20th Anniversary Festival key visual illustrated by Yukiko Hirai

[would-you-punt-them]

Math

Before you punt, we need to calculate at what speed your target will need to be moving to escape the Earth's gravitational field.

First, we need the mass (M) and radius (r) of planet Earth. If we assume the Earth maintains a constant density and is perfectly spherical (neither of which is true) the estimated mass of the planet is around 5.972 x 10^24 kilograms, with an average radius of 6.371 x 10^6 metres.

We also need the approximate value of Newton's gravitational constant (G), which is around (6.674 x 10^-11 m^3 kg^-1 s^-2).

Escape velocity (v) is the square root of (2 x Newton's gravitational constant x Earth's mass) / Earth's radius.

As an equation, that's (v = √((2GM) / r)).

So, v = √((2 x (6.674 x 10^-11 m^3 kg^-1 s^-2) x (5.972 x 10^24 kg)) / (6.371 x 10^6 m)).

v = √(((2 x (6.674 m^3 kg^-1 s^-2) x (5.972 kg)) / (6.371 m)) x 10^7)

v = √(((2 x (6.674 kg^-1 s^-2) x (5.972 kg)) / (6.371)) x 10^7 m^2)

v = √(((2 x (6.674 s^-2) x (5.9722)) / (6.371)) x 10^7 m^2)

v = √(((2 x (6.674) x (5.972)) / (6.371)) x 10^7 m^2 s^-2)

v = √(((2 x (6.674) x (5.972)) / (6.371)) x 10^7) m/s

so, to three significant figures:

v = 11,200 metres per second

Now, the Sun is 92 million miles away, so, if we take-

[upennmanuscripts]

LJS 26 is a 13th century manuscript that includes a treatise on the fundamentals of arithmetic (Algorismus), followed by a treatise on cosmography that describes and illustrates the Ptolemaic model of a spherical earth divided into climactic zones at the center of the concentric spheres of the universe.

🔗:

[maths-screaming]

"Check Your Work"

All my elementary teachers wrote the same thing on my report cards:

"Makes careless mistakes because she does not check her work."

I could write a book about how having undiagnosed, untreated ADHD was the primary problem here. But I'll skip that for now.

Instead, I want to talk about a secondary problem with "does not check her work."

To do it, let's look at this example from a few posts ago:

Here, I made the mistake of adding the tens instead of subtracting them, which temporarily gave me "84" instead of the correct answer, "4." I caught it when I started a number line to check that 43 is 4 away from 39 and realized that there was no way I'd need to write out 80+ numbers to figure that out.

At the time, I wrote: I guarantee you that 7 year old me would not have caught that mistake, because 7 year old me would have been expected not to do something as concrete as a number line to check their work.

Here's what I want to talk about:

I'm not sure what 7 year old me was expected to do to "check their work."

I didn't know then, and I don't know now. I think we were supposed to look at our work and find obvious mistakes? Like, I was supposed to look at 43 - 39 and say to myself "wow, that cannot possibly be 80something"? I guess?

But were were never given any strategies to do that.

I'm new to the "counting on" number-line approach; we were never shown how to do those. We weren't even told "add the answer to the bottom number to get the top one" until middle school. I know, because I vividly remember that being a revelation to me. You can just add the numbers back together to get the number? Why did no one tell me this??

So when told to "check my work," I didn't, because I didn't know how. I couldn't tell from looking at it when it was wrong; I needed concrete alternative "proofs," which I was never taught to do. I lacked the number sense to figure them out myself. And, at age 7, I lacked the self-awareness to say "what do you mean by check your work, because I have no idea how to do that."

(I also grew up in an era, and with parents, that would have seen "what do you mean? I don't get it" as impermissible "backtalk," worthy of a "go to your room without dinner." But that is yet another entire book.)

Again, I'm pretty sure non-dyscalculic kids can look at 43 - 39 and say "that can't be 80something if you subtracted." Non-dyscalculic kids can probably also say "I checked by counting and 43 is 4 away from 39." An expert would likely read this post and say "yeah, you have weak number sense."

The problem is that at age 7, there was no way for me to know my number sense wasn't on par with my peers'. And no one with the knowledge or perspective to deduce that fact appears to have done so. So I kept on "making careless mistakes because she does not check her work."

[corincadence828]

Solve 6÷2(1+2)

do it. prove you know or don’t know math. only cowards won’t try.

[english-lessons-bolzano]

Names for the number 0 in English

"Zero" is the usual name for the number 0 in English. In British English "nought" is also used and in American English "naught" is used occasionally for zero, but (as with British English) "naught" is more often used as an archaic word for nothing. "Nil", "love", and "duck" are used by different sports for scores of zero.

There is a need to maintain an explicit distinction between digit zero and letter O,[a] which, because they are both usually represented in English orthography (and indeed most orthographies that use Latin script and Arabic numerals) with a simple circle or oval, have a centuries-long history of being frequently conflated. However, in spoken English, the number 0 is often read as the letter "o" ("oh"). For example, when dictating a telephone number, the series of digits "1070" may be spoken as "one zero seven zero" or as "one oh seven oh", even though the letter "O" on the telephone keypad in fact corresponds to the digit 6.

In certain contexts, zero and nothing are interchangeable, as is "null". Sporting terms are sometimes used as slang terms for zero, as are "nada", "zilch" and "zip".

Zero" and "cipher"

"Zero" and "cipher" are both names for the number 0, but the use of "cipher" for the number is rare and only used in very formal literary English today (with "cipher" more often referring to cryptographic cyphers). The terms are doublets, which means they have entered the language through different routes but have the same etymological root, which is the Arabic "صفر" (which transliterates as "sifr"). Via Italian this became "zefiro" and thence "zero" in modern English, Portuguese, French, Catalan, Romanian and Italian ("cero" in Spanish). But via Spanish it became "cifra" and thence "cifre" in Old French, "cifră" in Romanian and "cipher" in modern English (and "chiffre" in modern French).

"Zero" is more commonly used in mathematics and science, whereas "cipher" is used only in a literary style. Both also have other connotations. One may refer to a person as being a "social cipher", but would name them "Mr. Zero", for example.

In his discussion of "naught" and "nought" in Modern English Usage, H. W. Fowler uses "cipher" to name the number 0.

O" ("oh")

In spoken English, the number 0 is often read as the letter "o", often spelled oh. This is especially the case when the digit occurs within a list of other digits. While one might say that "a million is expressed in base ten as a one followed by six zeroes", the series of digits "1070" can be read as "one zero seven zero", or "one oh seven oh". This is particularly true of telephone numbers (for example 867-5309, which can be said as "eight-six-seven-five-three-oh-nine"). Another example is James Bond's designation, 007, which is always read as "double-o seven", not "double-zero seven", "zero-zero seven", or "o o seven".

The letter "o" ("oh") is also used in spoken English as the name of the number 0 when saying times in the 24-hour clock, particularly in English used by both British and American military forces. Thus 16:05 is "sixteen oh five", and 08:30 is "oh eight thirty".

The use of O as a number can lead to confusion as in the ABO blood group system. Blood can either contain antigen A (type A), antigen B (type B), both (type AB) or none (type O). Since the "O" signifies the lack of antigens, it could be more meaningful to English-speakers for it to represent the number "oh" (zero). However, "blood type O" is properly written with a letter O and not with a number 0.

In sport, the number 0 can have different names depending on the sport in question and the nationality of the speaker.

"Nil" in British sports

Many sports that originated in the UK use the word "nil" for 0. Thus, a 3-0 score in a football match would be read as "three-nil".[1] Nil is derived from the Latin word "nihil", meaning "nothing", and often occurs in formal contexts outside of sport, including technical jargon (e.g. "nil by mouth") and voting results.

It is used infrequently in U.S. English, although it has become common in soccer broadcasts.

"Nothing" and "oh" in American sports

edit

In American sports, the term "nothing" is often employed instead of zero. Thus, a 3-0 score in a baseball game would be read as "three-nothing" or "three to nothing". When talking about a team's record in the standings, the term "oh" is generally used; a 3-0 record would be read as "three and oh".

In cricket, a team's score might read 50/0, meaning the team has scored fifty runs and no batter is out. It is read as "fifty for no wicket" or "fifty for none".

Similarly, a bowler's analysis might read 0-50, meaning he has conceded 50 runs without taking a wicket. It is read as "no wicket for fifty" or "none for fifty".

A batsman who is out without scoring is said to have scored "a duck", but "duck" is used somewhat informally compared to the other terms listed in this section. It is also always accompanied by an article and thus is not a true synonym for "zero": a batter scores "a duck" rather than "duck".

A name related to the "duck egg" in cricket is the "goose egg" in baseball, a name traced back to an 1886 article in The New York Times, where the journalist states that "the New York players presented the Boston men with nine unpalatable goose eggs", i.e., nine scoreless innings.

"Love" and "bagel" in tennis

In tennis, the word "love" is used to replace 0 to refer to points, sets and matches. If the score during a game is 30-0, it is read as "thirty-love". Similarly, 3-0 would be read as "three-love" if referring to the score during a tiebreak, the games won during a set, or the sets won during a match. The term was adopted by many other racquet sports.

There is no definitive origin for the usage. It first occurred in English, is of comparatively recent origin, and is not used in other languages. The most commonly believed hypothesis is that it is derived from English speakers mis-hearing the French l'œuf ("the egg"), which was the name for a score of zero used in French because the symbol for a zero used on the scoreboard was an elliptical zero symbol, which visually resembled an egg.

Although the use of "duck" in cricket can be said to provide tangential evidence, the l'œuf hypothesis has several problems, not the least of which is that in court tennis the score was not placed upon a scoreboard. There is also scant evidence that the French ever used l'œuf as the name for a zero score in the first place. (Jacob Bernoulli, for example, in his Letter to a Friend, used à but to describe the initial zero–zero score in court tennis, which in English is "love-all".) Some alternative hypotheses have similar problems. For example, the assertion that "love" comes from the Scots word "luff", meaning "nothing", falls at the first hurdle, because there is no authoritative evidence that there has ever been any such word in Scots in the first place.

According to the Oxford English Dictionary, the first use of the word "love" in English to mean "zero" was to define how a game was to be played, rather than the score in the game itself. Gambling games could be played for stakes (money) or "for love (of the game)", i.e., for zero stakes. The first such recorded usage quoted in the OED was in 1678. The shift in meaning from "zero stakes" to "zero score" is not an enormous conceptual leap, and the first recorded usage of the word "love" to mean "no score" is by Hoyle in 1742.

In recent years, a set won 6-0 ("six-love") has been described as a bagel, again a reference to the resemblance of the zero to the foodstuff. It was popularised by American announcer Bud Collins.

Null

In certain contexts, zero and nothing are interchangeable, as is "null". However, in mathematics and many scientific disciplines, a distinction is made (see null). The number 0 is represented by zero while null is a representation of an empty set {}. Hence in computer science a zero represents the outcome of a mathematical computation such as 2−2, while null is used for an undefined state (for example, a memory location that has not been explicitly initialised).

In English, "nought" and "naught" mean zero or nothingness, whereas "ought" and "aught" (the former in its noun sense) strictly speaking mean "all" or "anything", and are not names for the number 0. Nevertheless, they are sometimes used as such in American English; for example, "aught" as a placeholder for zero in the pronunciation of calendar year numbers. That practice is then also reapplied in the pronunciation of derived terms, such as when the rifle caliber .30-06 Springfield (introduced in 1906) is accordingly referred to by the name "thirty-aught-six".

The words "nought" and "naught" are spelling variants. They are, according to H. W. Fowler, not a modern accident as might be thought, but have descended that way from Old English. There is a distinction in British English between the two, but it is not one that is universally recognized. This distinction is that "nought" is primarily used in a literal arithmetic sense, where the number 0 is straightforwardly meant, whereas "naught" is used in poetical and rhetorical senses, where "nothing" could equally well be substituted. So the name of the board game is "noughts & crosses", whereas the rhetorical phrases are "bring to naught", "set at naught", and "availeth naught". The Reader's Digest Right Word at the Right Time labels "naught" as "old-fashioned".

Whilst British English makes this distinction, in American English, the spelling "naught" is preferred for both the literal and rhetorical/poetic senses.

"Naught" and "nought" come from the Old English "nāwiht" and "nōwiht", respectively, both of which mean "nothing". They are compounds of no- ("no") and wiht ("thing").

The words "aught" and "ought" (the latter in its noun sense) similarly come from Old English "āwiht" and "ōwiht", which are similarly compounds of a ("ever") and wiht. Their meanings are opposites to "naught" and "nought"—they mean "anything" or "all". (Fowler notes that "aught" is an archaism, and that "all" is now used in phrases such as "for all (that) I know", where once they would have been "for aught (that) I know".)

However, "aught" and "ought" are also sometimes used as names for 0, in contradiction of their strict meanings. The reason for this is a rebracketing, whereby "a nought" and "a naught" have been misheard as "an ought" and "an aught".

sometimes used as names for 0, in contradiction of their strict meanings. The reason for this is a rebracketing, whereby "a nought" and "a naught" have been misheard as "an ought" and "an aught".

Samuel Johnson thought that since "aught" was generally used for "anything" in preference to "ought", so also "naught" should be used for "nothing" in preference to "nought". However, he observed that "custom has irreversibly prevailed in using 'naught' for 'bad' and 'nought' for 'nothing'". Whilst this distinction existed in his time, in modern English, as observed by Fowler and The Reader's Digest above, it does not exist today. However, the sense of "naught" meaning "bad" is still preserved in the word "naughty", which is simply the noun "naught" plus the adjectival suffix "-y". This has never been spelled "noughty".

The words "owt" and "nowt" are used in Northern English. For example, if tha does owt for nowt do it for thysen: if you do something for nothing do it for yourself.

The word aught continues in use for 0 in a series of one or more for sizes larger than 1. For American Wire Gauge, the largest gauges are written 1/0, 2/0, 3/0, and 4/0 and pronounced "one aught", "two aught", etc. Shot pellet diameters 0, 00, and 000 are pronounced "single aught", "double aught", and "triple aught". Decade names with a leading zero (e.g., 1900 to 1909) were pronounced as "aught" or "nought". This leads to the year 1904 ('04) being spoken as "[nineteen] aught four" or "[nineteen] nought four". Another acceptable pronunciation is "[nineteen] oh four".

Decade names

See also: Aughts

While "2000s" has been used to describe the decade consisting of the years 2000–2009 in all English speaking countries, there have been some national differences in the usage of other terms.

On January 1, 2000, the BBC listed the noughties (derived from "nought") as a potential moniker for the new decade. This has become a common name for the decade in the U.K.and Australia, as well as some other English-speaking countries. However, it has not become the universal descriptor because, as Canadian novelist Douglas Coupland pointed out early in the decade, "[Noughties] won't work because in America the word 'nought' is never used for zero, never ever".

The American music and lifestyle magazine Wired favoured "Naughties", which they claim was first proposed by the arts collective Foomedia in 1999.However, the term "Naughty Aughties" was suggested as far back as 1975 by Cecil Adams, in his column The Straight Dope.

interchangeable, as is "null". However, in mathematics and many scientific disciplines, a distinction is made (see null). The number 0 is represented by zero while null is a representation of an empty set {}. Hence in computer science a zero represents the outcome of a mathematical computation such as 2−2, while null is used for an undefined state (for example, a memory location that has not been explicitly initialixed).

Slang

Sporting terms (see above) are sometimes used as slang terms for zero, as are "nada", "zilch" and "zip".

"Zilch" is a slang term for zero, and it can also mean "nothing". The origin of the term is unknown.

Silvio Pasqualini Bolzano inglese ripetizioni English insegnante teacher

[tragediambulante]

Arithmetic from the Borgia aparments, Pinturicchio, 1492-94

[noosphe-re]

[thecrabbybarista]

Okay math side of Tumblr I need help

So I was reading Broca's Brain by Carl Sagan yesterday, and there's this point where Sagan lists off a few bizarre scientific facts as examples of how true science is often more interesting and whimsical than anything a hack pseudoscientist could make up.

One of these facts was that there's a logically sound arithmetic in which 2 times 1 is not equal to 1 times 2. This piqued my interest, so I took to Firefox and Wikipedia to figure out more, but I searched up a few things and couldn't find anything helpful.

So does anyone here know what he's talking about and how that works?

[lukavelimirov]

The allegory of arithmetic. Engraving from "The Pearl of Philosophy" by Gregor Reisch, 1503.

On the right in the foreground, Pythagoras uses a counting board with chips.

Counting tokens appeared in the Middle Ages, initially they were used for arithmetic calculations on chalkboards, including in accounting. Their appearance is associated with the name of Herbert of Avrilacqua (c. 946-1003), the future Pope Sylvester II. It was he who recommended using special quasi—coins with Roman numerals or special numerical signs - vertices for counting on the boards. This is how counting tokens appeared, and they were also made by money minters.

In many countries, tokens were used as a bargaining chip. With the advent of the first banks in Italy in the 13th century, they began to be actively used by bankers, money changers and merchants. Some French banknotes were minted at state mints, and royal portraits were often depicted on their obverse. It was difficult to distinguish such tokens from ordinary copper money — they probably circulated with them. In Germany, tokens were actively used in card games as money substitutes, similar to modern casino chips.

Over the course of several centuries, thousands of varieties of tokens of various types and from all kinds of materials have been minted in different parts of Europe: alloys of copper, bronze, brass, tinplate, base silver and souvenirs — even gold. Counting tokens existed until the 19th century, when people all over Europe learned to count in a column and to themselves.