Visualizing Math

A blog dedicated to mathematics. 

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*realizes joy division did some real quick fs photoelectron spectroscopy for their dumb album cover*


Geometry Matters:

Various nature elements that abide by geometric laws and construction patterns.

© Geometrymatters,2014

Reblogged for the Visualizing Math followers that are fans of Sacred Geometry.


Today’s Gender of the Day is: Bertrand Russell and Alfred North Whitehead Proving That 1+1=2 

(via mathematica)


This is the graph of |x|+|y|=4. I like it.


This is the graph of |x|+|y|=4. I like it.


What do leopard spots, striped marine angelfish, and sand dune ripples have in common? Their patterns are self-organizing Turing systems! Discovered by Alan Turing in the 1950s, these repeating natural patterns can be created by the interaction of two things that spread at different speeds, one faster than the other.

I knew that name was familiar! Alan Turing is quite an interesting person. Wikipedia lists him as “a British mathematician, logician, cryptanalyst, philosopher, computer scientist, mathematical biologist, and marathon and ultra distance runner”! Furthermore, “Winston Churchill said that Turing made the single biggest contribution to Allied victory in the war against Nazi Germany” cracking codes! Read about him!

Submitted by TheFrankensTeam:

In the model you can change the number of dots and the deviation too. If you set the “type demo” to dynamic it will make possible to analyse how the wave-pattern changes when deviation grows.


Imagine you wanted to measure the coastline of Great Britain. You might remember from calculus that straight lines can make a pretty good approximation of curves, so you decide that you’re going to estimate the length of the coast using straight lines of the length of 100km (not a very good estimate, but it’s a start). You finish, and you come up with a total costal length of 2800km. And you’re pretty happy. Now, you have a friend who also for some reason wants to measure the length of the coast of Great Britain. And she goes out and measures, but this time using straight lines of the length 50km and comes up with a total costal length of 3400km. Hold up! How can she have gotten such a dramatically different number?

It turns out that due to the fractal-like nature of the coast of Great Britain, the smaller the measurement that is used, the larger the coastline length will be become. Empirically, if we started to make the measurements smaller and smaller, the coastal length will increase without limit. This is a problem! And this problem is known as the coastline paradox.

By how fractals are defined, straight lines actually do not provide as much information about them as they do with other “nicer” curves. What is interesting though is that while the length of the curve may be impossible to measure, the area it encloses does converge to some value, as demonstrated by the Sierpinski curve, pictured above. For this reason, while it is a difficult reason to talk about how long the coastline of a country may be, it is still possible to get a good estimate of the total land mass that the country occupies. This phenomena was studied in detail by Benoit Mandelbrot in his paper “How Long is the Coast of Britain" and motivated many of connections between nature and fractals in his later work.

(via mathematica)

The AAT Project™ is an online competition that will identify, mentor and manage exceptional teens whose ideas will change the world. It aims to promote technological and scientific innovation, and change the cultural aspect of what science and math look like by setting a new higher standard for teen role models. If you’re a teen with a world-changing idea, sign up on their splash page and see if you’ve got what it takes to win the ultimate competition!
The Grand Prize winner will not only receive instruction from their vast selection of academic professionals, marketing advice from industry experts on how to turn the idea into a profitable enterprise, and a provisional patent while the idea is still in the works, but will also receive $75,000. In addition to the Grand Prize winner, there will also be a People’s Choice Award winner, who is chosen solely by the online voting public, and will receive $25,000, and 12 monthly finalists, who will receive $1,000 each and a mini-documentary and a cumulative documentary by Academy Award-winning documentary filmmaker Ross Kauffman.
It is from these 12 monthly finalists that the Grand Prize winner will be chosen, by the competition’s distinguished judges and the online voting public. Their great achievement will be announced on a nationally televised special (to which they and their fellow finalists will be invited) that will feature America’s top celebrities and performers.  
Find out more about their contest here, and follow their TumblrFacebook page, Twitter, and Instagram
Note: I didn’t get paid to post this. I’m genuinely interested in seeing teens delve into science, technology, engineering, and (of course!!!) mathematics. If you have a good idea and are too lazy to act on it, let this prize be an incentive…and maybe you’ll end up changing the world while you’re at it. 


Illustrator Florian Nicolle breaks down break dancing.


Numbers are simple.


Numbers are simple.


“Phyllotactic Portrait of Fibonacci” by Robert Bosch

Mathematical artist Robert Bosch created this picture by adapting a well-known portrait of the Italian mathematician Leonardo Pisano Bigollo (c. 1170—1250), who was better known as Fibonacci.

Fibonacci described the sequence that bears his name in his 1202 book Liber Abaci, although the sequence was known to Indian mathematicians as early as the 6th century. The Fibonacci sequence begins 1, 1, 2, 3, 5, 8, 13, 21, the key property being that each of the terms from the third term onwards is the sum of the preceding two terms. 

Fibonacci used his sequence to study the growth of a population of rabbits, under idealising assumptions. The sequence can be used to model various biological phenomena, including the arrangement of leaves on a stem, which is known as phyllotaxis. Robert Bosch used a model of phyllotaxis to produce this picture. He explains:

Using a simple model of phyllotaxis (the process by which plant leaves or seeds are arranged on their stem), I positioned dots on a square canvas. By varying the radii of the dots, I made them resemble Fibonacci. Incidentally, the number of dots, 6765, is a Fibonacci number. So are the number of clockwise spirals (144) and counterclockwise spirals (233) formed by the dots. 

A framed version of this picture is currently being exhibited at the Bridges Exhibition at Gwacheon National Science Museum, Seoul. You can read more about the picture here: The same page discusses another version of the picture, also by Robert Bosch, but this time illustrating the Travelling Salesman problem. +Patrick Honner has posted about the other version of the picture here:

Relevant links

Robert Bosch’s website: 

Wikipedia on Leonardo Fibonacci:

The On-Line Encyclopedia of Integer Sequences on the Fibonacci numbers:

Fibonacci numbers in nature:

As well as featuring in this picture, the Fibonacci number 6765 is the name of an asteroid:

“We’re also a band.” (

(Found via +Patrick Honner.)

#art #artist #mathematics #scienceeveryday

(via geometric-aesthetic)


Parametric curves by[R-D]

La mia arte matematica. Queste figure ricordano vecchi merletti, solo che sono ottenute attraverso  equazioni.



"Fibonacci Sequence #3" Art print

Leonardo Fibonacci is an Italian mathematician from the 12th century.

Asker Anonymous Asks:
Love the blog unfortunately I don't possess the grasp of mathematics to pick it all up, sigh, anyway, nice blog
visualizingmath visualizingmath Said:

Thank you, and please don’t be so discouraged, Anon. If you love and enjoy the blog, then I think you must be grasping/picking up enough things. 



Inspired by this twocubes’ post and asked to make a animation of it, I made a gif.

:3 this is pretty

(you could have @mentioned me or tagged me so that I could have noticed this earlier tho :V)