Fractal Designs

from mathmajik.tumblr.com:

"Fascinated by the intricate patterns formed by fractals, basically math processes that repeat incessantly in an ongoing feedback loop, UK physicist-turned-web developer Tom Beddard makes impossibly elaborate complexes that look like they belong in the gritty cities of a dystopian fantasy. Basically what he does is write and run programs on his computer that spit out patterns—"the best outcomes are often the least expected!“ he writes—that he in turn massages (by way of shadowing and the like) into looking like faceted steel-and-concrete architecture.

Sources:
Curbed.com
Architizer.com"

Rotation

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Geometric Distribution

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How to Cut a Pizza

How to cut a pizza into 11 slices of equal size. Via Quora. 

Ben Franklin's Magic Squares

“'Magic Squares and Linear Algebra' by Christopher J. Henrich in the American Mathematical Monthly, Vol 98, no 6, 1991 has a very interesting 16x16 magic square created by Benjamin Franklin.

Although the diagonals of this square do not sum to 2056, there are many other magical properties. Henrich quotes Franklin as having said, “[it] is the most magically magical of any magic square ever made by any magician.”

All the rows and columns sum to the number 2056, but that is not all. Half rows and half columns sum to 1028.

The sixteen entries in every 4x4 subsquare sum to 2056.

But there is even more!

In the figures above, the bent diagonals going from top to bottom (Figure 1) sum to 2056. Even the broken ones that have two pieces! Follow the colored patterns and you will be able to check this. The other three figures show the other diagonals going from from right to left (Figure 2), from bottom to top (Figure 3) and from left to right (Figure 4) also have sums of 2056.

This magic square was constructed over 200 years ago. Even with the aid of a computer this would be a prodigious task.

Source: math.wichita.edu"

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Pi

Pi

Math is the universal language of the universe.

Art is the universal visual language of humans.

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Angles in Curved Spaces

Three 90 degree angles in a curved space.

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Geometric Images

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Snapology

Heinz Strobl invented a technique called “snapology” or “knotology”, to fold paper strips into all kind of shapes you can imagine. The idea is illustrated here, for instance.

In the image above, you can imagine hexagons (in orange) and pentagons (in purple) surrounding the vertices. A curious mathematical fact is that you can vary the number of hexagons quite freely, but not the number of pentagons: there must always be 12 pentagons to fit into a perfect shape. To prove this, you need to play around with Euler’s polyhedral formula.

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Does this make you feel small?

A model of how many Earths would fit in the Sun.

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Pick a number...

Pick a number between 1 and 99, write it as a word, then count the letters to get a new number. Write the new number as a word, and count its letters- repeat.  This curiosity was tweeted by@IanMathmogician, and if you try it you’ll find you get stuck at the number 4- the only number equal to its letter-count.  This image shows the network of what  your possible routes to 4 could be. It shows you’ll always get there after 5 steps.

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Mathematical Pasta

Created by a team of designers, ‘Pasta by Design’ book reveals the hidden mathematical beauty of pasta: its geometrical shapes and surfaces are explained by mathematical formulae, drawings and illustrations - source

Angles, angles, everywhere

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Making Wearables from E-Waste

Cyrus Kabiru is an artist from Nairobi, Kenya who is turning e-waste into wearables and art.

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Here is a short video interview with Cyrus:

The Boy Who Harnessed the Wind

From ultrafacts.tumblr.com:

William had a dream of bringing electricity and running water to his village. And he was not prepared to wait for politicians or aid groups to do it for him. The need for action was even greater in 2002 following one of Malawi’s worst droughts, which killed thousands of people and left his family on the brink of starvation.

Unable to attend school, he kept up his education by using a local library. Fascinated by science, his life changed one day when he picked up a tattered textbook and saw a picture of a windmill. Mr Kamkwamba told the BBC News website: “I was very interested when I saw the windmill could make electricity and pump water.

“I thought: ‘That could be a defense against hunger. Maybe I should build one for myself’.” When not helping his family farm maize, he plugged away at his prototype, working by the light of a paraffin lamp in the evenings. But his ingenious project met blank looks in his community of about 200 people.

“Many, including my mother, thought I was going crazy,” he recalls. “They had never seen a windmill before.” [x]

In 2014, William Kamkwamba received his 4 year degree at Dartmouth College in Hanover, New Hampshire where he was a student.

Read more at http://news.bbc.co.uk/2/hi/africa/8257153.stm

Transluscent Succulent Haworthia cooperi ‘Dodson’

image source

Positivity through Minimalism

"Photographer Peechaya Burroughs' playfully minimalistic shots contain a contagious amount of positivity. Through Burroughs' unique lens, a yellow/orange balloon becomes a perfect egg yolk, food is transformed into artistic material, and origami is magically brought to life. No matter what the concept, each image showcases the artist's imaginative ability to see the extraordinary in everyday items.

"My photographs mainly consist of things that I create or manipulate by hand," Burroughs explains on her website. "Occasionally I use Photoshop when enhancing the idea. Driven by childhood memories and very much fascinated by children’s imagination and their quirkiness, the direction of my photography is light, easy to approach with a little touch of everyday optimism."

On the surface, her portfolio may appear modest and quite simple, but its whimsical nature is what sets it apart. Since optimism is a key component, it's no wonder that the photographer has been able to prove that ordinary objects have the potential to become brilliant works of art." mymodernmet