#euler spiral

[arbieroo-art]

Euler spirals.

[inksandpensblog]

[me, seeing the AvGeometry thumbnail]: they’re finally doing Fibonacci

(also I must say that desk mats are the most appropriate merch for this series ever)

okay there’s no excuse not to make fanart anymore now that we know we can just make a single colored line, we don’t even have to make a whole stickfigure this is taking “golden ratio” literally

oh neat so that’s why φ moved like that in AvMath. I’d thought it seemed like it was moving on a line and I was right, we just couldn’t see the line then

this is when I realized how happy I was and I had to remind myself that I hate doing math

oh the inside of the shape goes golden too. φ can leave the lines and float inside it when it does, which is interesting

I’m curious if Euler told Fibonacci about Orange at all, I can’t tell if φ is messing with Orange for fun or showing him who’s boss or just over-excited and going on a visual info-dump about its interests

what

why is it dubstep

what is this thing supposed to be?! I don’t remember learning about anything like this in math

that spiral was so satisfying though. never would’ve expected it to be accompanied by a fade-out from dubstep

OH THEY’RE SYNCHING NOW. THEY’RE CHOREOGRAPHING TO THE BEAT

I replayed the drawing of the glider several times, the sounds in that sequence just fell into place perfectly

math having a natural enemy is such a strange concept to entertain XD

the way the pentagon fractals when it breaks

Orange crafting again

ooh what do the other colors mean?

CONTINUITY?!

[dorkichiban]

By cutting a sphere along a spiral with width 1 / N and flattening out the resulting shape we create a Euler spiral when N tends to the infinity. In other words we can create a map projection whose distortion tends to zero as N tends to the infinity.

finally, a good fucking map projection:

[c0rpseductor]

sorry for blogging about this New Website Journey. idk why. im shy. Anyway

there's an intelligence kink group on here. i am not a sapiosexual but i am a pedant so i feel it may become dangerous for me

specifically someone was asking about like, "what is the closest phenomenon to explaining everything about life" and started going on about euler's spiral being in a bunch of stuff. i'm like, so close! you have noticed a pattern, not a model with any explanatory power.

anyway i actually do not want to annoy these people but i have to get it out somewhere: physics. you can technically model everything that way and thus "explain" all phenomena although it gets like. useless to the human brain, in terms of actual comprehension. but like the conjecture that Everythign Is A Simulation!!!!1 is bc you can technically reduce everything to math and model it On Da Computer. what fucking worm have they done this to, i remember reading a post where they made it possible to simulate the entire brain of a specific species of worm or some shit.

i barely remember anything about theoretical physics and likely didn't understand it adequately in middle school, and i'm not a mathematician, so i have only the slightest understanding of wtf im talking about, but i used to love this concept so i felt like if i didnt say it somewhere i was gonna die. ok. thank you for tolerating my fl adventure

[bsahely]

The Spiral of Coherence: A Harmonic Cosmology of Life, Grace, and Becoming | ChatGPT4o

[Download Full Document (PDF)] “The universe is not a place — it is a process of spiraling coherence, where phase and form, love and logic, healing and meaning unfold as One.” This work offers a unified vision of reality through the lens of the Spiral of Coherence, integrating cosmology, consciousness, healing, governance, and inner transformation. Drawing from Fourier analysis, Euler’s identity,…

[earthvitalsignimpact]

Fibonacci Fun Quiz: Unlock the Secrets of Nature’s Hidden Code!

by UEVS & the creative power of AI

Test your knowledge of the Fibonacci Sequence and its incredible presence in nature, the cosmos, and even molecular structures!

🧠 Section 1: Multiple Choice

What is the first number in the Fibonacci Sequence? a) 1 b) 0 c) 2 d) 3

Which ratio does the Fibonacci Sequence approximate as it progresses? a) 3.1416 (Pi) b) 1.618 (Golden Ratio) c) 2.718 (Euler’s Number) d) 0.577 (Euler-Mascheroni Constant)

Which of the following natural phenomena follows Fibonacci patterns? a) The arrangement of sunflower seeds b) The shape of the Great Pyramid c) The orbit of the Moon around Earth d) The pattern of raindrops in a storm

Where can Fibonacci spirals be observed in the cosmos? a) The structure of black holes b) The spiral arms of galaxies c) The shape of comets’ tails d) The way stars twinkle

In which field has the Fibonacci Sequence been used to analyze market trends? a) Astronomy b) Economics c) Medicine d) Cryptography

🔢 Section 2: True or False

The Fibonacci Sequence can be found in the structure of DNA. 🔲 True 🔲 False

Golden Ratio proportions can only be found in nature, not in man-made art or architecture. 🔲 True 🔲 False

The Fibonacci Sequence applies to quantum physics, influencing atomic-level structures. 🔲 True 🔲 False

The Fibonacci spiral is just a human-made concept with no real-world applications. 🔲 True 🔲 False

The number of petals on most flowers often follows Fibonacci numbers. 🔲 True 🔲 False

🌀 Section 3: Short Answer

What are the first six numbers in the Fibonacci Sequence? Answer: __

Name one famous artist or architect who used the Golden Ratio in their work. Answer: __

Why do many natural forms follow the Fibonacci Sequence? Answer: __

What is another name for the Golden Ratio? Answer: __

If a new species of alien plant is discovered, and it follows Fibonacci spirals, what might be the mathematical reason behind this? Answer: __

🎉 Bonus Question (For the Fibonacci Masters!)

If Fibonacci’s rabbits kept breeding at the same rate, what would be the population after 10 generations? Answer: __ (Hint: Use the sequence!)

Fibonacci Fun Quiz – Answer Key

🧠 Section 1: Multiple Choice

What is the first number in the Fibonacci Sequence? ✅ b) 0

Which ratio does the Fibonacci Sequence approximate as it progresses? ✅ b) 1.618 (Golden Ratio)

Which of the following natural phenomena follows Fibonacci patterns? ✅ a) The arrangement of sunflower seeds

Where can Fibonacci spirals be observed in the cosmos? ✅ b) The spiral arms of galaxies

In which field has the Fibonacci Sequence been used to analyze market trends? ✅ b) Economics

🔢 Section 2: True or False

The Fibonacci Sequence can be found in the structure of DNA. ✅ True (DNA’s double helix follows Fibonacci-based proportions)

Golden Ratio proportions can only be found in nature, not in man-made art or architecture. ✅ False (Leonardo da Vinci, the Parthenon, and many Renaissance artists used it)

The Fibonacci Sequence applies to quantum physics, influencing atomic-level structures. ✅ True (Electron orbits and quantum waves exhibit Fibonacci patterns)

The Fibonacci spiral is just a human-made concept with no real-world applications. ✅ False (It appears in nature, galaxies, and biological growth patterns)

The number of petals on most flowers often follows Fibonacci numbers. ✅ True (Many flowers have petal counts of 3, 5, 8, 13, etc.)

🌀 Section 3: Short Answer

What are the first six numbers in the Fibonacci Sequence? ✅ 0, 1, 1, 2, 3, 5

Name one famous artist or architect who used the Golden Ratio in their work. ✅ Leonardo da Vinci, Le Corbusier, Salvador Dalí, or the designers of the Parthenon

Why do many natural forms follow the Fibonacci Sequence? ✅ It optimizes growth, energy efficiency, and spatial arrangement in nature.

What is another name for the Golden Ratio? ✅ Phi (Φ)

If a new species of alien plant is discovered, and it follows Fibonacci spirals, what might be the mathematical reason behind this? ✅ It maximizes space efficiency, nutrient absorption, and light exposure—just like plants on Earth!

🎉 Bonus Question (For the Fibonacci Masters!)

If Fibonacci’s rabbits kept breeding at the same rate, what would be the population after 10 generations? ✅ 55 (Following the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55)

🔢 Score Breakdown:

13-16 Correct: 🎖️ Fibonacci Genius! You’ve unlocked the code of the universe!

9-12 Correct: 🌟 Golden Ratio Enthusiast! You see nature’s patterns.

5-8 Correct: 🔍 Fibonacci Explorer! Keep spiraling toward deeper knowledge.

0-4 Correct: 🤔 Math Maverick in Training! Time to crack the Fibonacci mystery!

[theam-cjsw]

The AM: April 29, 2024

A meandering Monday morning, with a throwback to the one-and-only Moondog, a nod to late Quebecois singer-songwriter Jean-Pierre Ferland, and an hour of Cosmic American Music to wrap the show. That plus the usual strains of ambient electronics, meditative jazz, post-rock interludes, and other songs to start your week on solid footing.

Soundcloud and Spotify streams are after the break, along with the full track list. Or you can stream it direct from CJSW, your favourite campus and community station.

Hour One

Bron Ut Små Vågor, Henrik von Euler • Små Vågor 6

Muted - Lehto Remix Tristan De Liège • Refractions (Remixed)

Kind of Light - Khotin Remix Bodywash • Single

Sing Together Salamanda • Single

Fly! Little Black Thing Yu Ching • The Crystal Hum

Nautical Miles Castle If • From the Sea

Mirror Images Bristol Manor • A Distant Urban Forest

Transpubliction My Kill Jack's On • 4 In '84

Night Sculpture Forest Swords • Bolted

Pools Steve Lyman, featuring Ben Lukas Boysen • Spiral

Hour Two:

We’ll live through the long, long days and the longnights (And when our last hour comes we’ll go quietly) Eiko Ishibashi • Drive My Car OST

Portrait of the Artist as a Thursday Charles Spearin • My City Of Starlings

Afternoon Moon Pie Torngat • La Petite Nicole

Apple Tree Hintermass • The Apple Tree

Cuckoo Hill Ellis Island Sound • The Good Seed

What’s the Most Exciting Thing Moondog • Moondog 2

Wine, Women and Song Moondog • Moondog 2

Love is Blue Paul Mauriat • Single

Le chat du café des artistes Jean-Pierre Ferland • Jaune

ESGGallin Samantha Savage Smith • Fake Nice

Disarray Nolan Potter • The Perils of Being Trapped Inside a Head

Pink Lite Ryan Bourne • Plant City

Hour Three:

One Step Forward, Two Steps Back Chet Sounds • Changes Happen To Everyone, Everywhere

All the Time Ghost Woman • Ghost Woman

Little More Time ROY • Spoons for the World

Strange Insistence Gun Outfit • Out of Range

Cowgirl Ora Cogan • Formless

Doggie Paddlin’ Thru the Cosmic Consciousness Psychic Temple • Doggie Paddlin’ Thru the Cosmic Consciousness

The sharp smell of cedar Field Works • Cedars

Worship the Sun (Not the Golden Boy) Fiver • Audible Songs from Rockwood

Sunrise John Hulbert • Opus III

Sunlight, Good Light Clinton St. John • The Minor Arkhana

[mathhombre]

One of my favorite ever math activities that I've come up with was just bringing a crate of Halos (clementine tangerines) into class. We measured them, then peeled them in one piece. They came up with their own classification system.

Then we found the area as best we could and used linear regression to make an area formula. Some did vs diameter, some vs circumference, and we got to discover clementine pi.

They found area by rearranging.

We should have submerged for volume!

In my most recent I was going for symmetry, and got an unfortunate facehugger.

The Euler spiral remains my favorite.

I'd love to see your peels...

IG

[mathsciencetuition]

What Prime Numbers Mean in Nature, Popular Culture, & the Internet

Prime numbers have captivated the imagination of mathematicians and scientists for centuries. These enigmatic numbers are not only essential in the field of mathematics but also find profound significance in various aspects of nature, popular culture, and the internet. At their core, prime numbers are integers greater than one that can only be divided by one and themselves without resulting in a fractional or decimal value. To explore the captivating world of prime numbers and excel in mathematics, students can benefit from specialized Maths tuition, such as that provided by the Miracle Learning Centre in Singapore. In this exploration, we will delve into the importance of prime numbers, uncovering their presence in the natural world, historical significance, cultural influences, and their ever-expanding role in the vast realm of the internet.

What are Prime Numbers?

Prime numbers are the fundamental building blocks of the natural numbers, and they play a crucial role in number theory and other branches of mathematics. An example of a prime number is 5, which can only be divided by 1 and 5, yielding a whole number quotient. In contrast, numbers like 4 or 6 can be divided by factors other than 1 and themselves, making them composite numbers.

The significance of prime numbers lies in their unique properties. They are infinite, and the distribution of prime numbers is a fascinating topic that has puzzled mathematicians for centuries. The prime number theorem, formulated in the 19th century, provides insights into how prime numbers become less frequent as numbers grow larger, but their irregular distribution defies any predictable pattern.

Importance of Prime Numbers:

Prime numbers hold immense significance in various aspects of mathematics and beyond. They serve as the foundational building blocks of number theory, cryptography, and other mathematical applications. Understanding prime numbers is essential for exploring and unlocking the mysteries of number patterns and mathematical relationships.

In addition to their mathematical importance, prime numbers have fascinating real-world applications. They play a vital role in encryption algorithms, ensuring secure communication and protecting sensitive data in the digital age. The study of prime numbers has also revealed their presence in nature, cultural expressions, and the internet, further highlighting their pervasive influence across diverse domains. The enigmatic nature of prime numbers continues to captivate mathematicians, scientists, and artists, making them a subject of endless exploration and fascination.

Prime Numbers in Nature:

Intriguingly, prime numbers also manifest in various aspects of the natural world. Some cicadas have life cycles that are prime number years long, which may be an adaptation to avoid synchronization with predators and increase their chances of survival. In the animal kingdom, prime numbers have been observed in the numbers of petals in certain flowers and the spirals of pinecones and sunflowers. These occurrences demonstrate the subtle yet remarkable presence of mathematical principles in the living world.

Prime Numbers in History:

Throughout history, prime numbers have captured the attention of mathematicians, leading to profound discoveries and breakthroughs. The ancient Greeks were among the first to explore prime numbers' properties, with Euclid proving that there are infinitely many primes around 300 BCE. The great mathematician Leonhard Euler made significant contributions to the study of primes in the 18th century, paving the way for further exploration in number theory.

Prime Numbers in Culture:

Beyond their mathematical significance, prime numbers have also permeated various cultural expressions. Writers, artists, musicians, and even filmmakers have drawn inspiration from these intriguing numbers. They have been used as symbols of mystery, uniqueness, and hidden patterns in literature, music, and visual arts. The fascination with prime numbers has made them a recurring motif in cultural works, connecting the abstract world of mathematics with the realm of human emotions and creativity.

Prime Numbers in the Internet:

In the digital age, prime numbers have gained newfound importance with the advent of cryptography and secure online communication. Large prime numbers serve as essential components of encryption algorithms, ensuring the confidentiality and integrity of data transmitted over the internet. Cryptographic systems, such as RSA encryption, rely on the computational difficulty of factoring the product of two large prime numbers, making it practically unfeasible for adversaries to break the code and access sensitive information.

Students can gain a deeper understanding of prime numbers and other fascinating mathematical concepts through specialized maths tuition. Enrolling in a Maths Tuition program, such as the one offered at Miracle Learning Centre in Singapore, can provide students with a structured and engaging learning environment. Expert maths teachers guide students through the intricacies of prime numbers, unraveling their significance in nature, culture, and the digital landscape.

Through interactive lessons, challenging exercises, and real-life examples, students can explore the enchanting world of mathematics, uncover interesting facts about prime numbers, and develop problem-solving skills that extend beyond the classroom. Maths tuition empowers students to embrace the beauty of numbers and inspires a lifelong appreciation for the wonders of mathematics.

Why Prime Numbers Matter?

The significance of prime numbers cannot be overstated, as they form the basis for essential applications in various fields. From secure communication and data protection to fundamental advances in number theory, prime numbers are at the core of numerous scientific and technological advancements. Understanding prime numbers can pave the way for groundbreaking discoveries and innovations, making them a vital area of study for mathematicians and researchers worldwide.

Understanding the profound importance of prime numbers can spark curiosity and interest in mathematics among students. Engaging in specialized maths tuition, such as the one provided by the Miracle Learning Centre in Singapore, can offer a unique opportunity for students to delve deep into the world of prime numbers under the guidance of expert Maths teachers in Singapore.

By enrolling in Maths Tuition in Singapore, students can unravel the enigmatic properties of prime numbers and their relevance in real-life applications. This learning experience empowers students to grasp complex concepts with ease, equipping them with invaluable mathematical skills and paving the way for future advancements and innovative solutions in the world of mathematics and beyond.

Some Interesting Facts about Prime Numbers:

The largest known prime number, as of my last update, is 2^82,589,933 - 1, a number with an astonishing 24,862,048 digits.

Prime numbers have fascinated mathematicians throughout history, with famous mathematicians like Gauss, Euler, and Ramanujan making significant contributions to the study of primes.

The twin prime conjecture proposes that there are infinitely many pairs of prime numbers that differ by 2, such as 3 and 5, 11 and 13, and so on.

The distribution of prime numbers follows no discernible pattern, making their occurrence appear random, yet their properties exhibit intriguing regularities.

Goldbach's conjecture, one of the oldest unsolved problems in number theory, states that every even integer greater than 2 can be expressed as the sum of two prime numbers.

Conclusion:

In conclusion, prime numbers hold a position of utmost importance in the realms of mathematics, nature, culture, and the internet. They form the backbone of number theory, cryptography, and various mathematical applications. Their presence in nature showcases the hidden mathematical order in the living world, while their influence on culture highlights the bridge between abstract concepts and human expression. Moreover, their role in securing internet communication has become indispensable in the digital age.

For those looking to grasp the true essence of prime numbers and their myriad applications, embarking on a journey of learning is essential. Students seeking to unravel the mysteries of mathematics can benefit from specialized maths tuition, such as that offered by the Miracle Learning Centre in Singapore. With the guidance of dedicated math teachers, students can explore the fascinating world of prime numbers and pave the way for future discoveries in this captivating field.

[arbieroo-art]

Irrational Euler spirals.

[art-of-mathematics]

Icosahedron net - "coiling up"

This icosahedron net is really cool, as it is just like a "string of triangles" you can just roll up to form the icosahedron.

Result:

- - -- ---

The hexagon grid is really helpful for drawing equilateral triangles.

- - -- ---

It reminds me of this:

Diffraction - Source: German PDF [found at TU-dresden website]

...

[low-sugar-eye-candy]

Wait for it... 

[enby-axels]

Rika Kihira - 2020 Nationals - Baby, God Bless You (x)

[ryanlj]

Euler Spiral Earth

[nofatclips]

Why do prime numbers make these spirals?