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Have fun playing with curvature

By Christian Lawson-Perfect. Posted September 14, 2014

Recently Tim Hutton and Adam Goucher have been playing around with hyperbolic tesselations. That has produced a {4,3,5} honeycomb grid for the reaction-diffusion simulator Ready, which Adam talked about on his blog a couple of days ago. Tim has also made a much simpler toy to play with in your browser: a visualisation of mirror tilings (the Wythoff construction) in spaces with different curvatures.

Hyperplay lets you select the kind of regular polygon you want to tile, and then your mouse controls the curvature of the space it sits in. Certain curvatures produce exact tilings of the space – for example, triangles tile a space with zero curvature – and you get projections of polyhedra for certain positive curvatures.

Radii of polyhedra

By Tom Button. Posted December 2, 2012

(At last month’s big MathsJam conference, we asked a few people who gave particularly interesting talks if they’d like to write something for the site. A surprising number said yes. First to arrive in the submissions pile was this piece by Tom Button.)

The formula for the surface area of a sphere, $A=4\pi r^{2}$, is the derivative of the formula for the volume of a sphere: $V=\frac{4}{3}\pi r^{3}$.

This result does not hold for a cube with side length $a$ if the surface area and volume are written in terms of $a$. However, if the surface area and volume are written in terms of half the side length, $r=\frac{a}{2}$, you get the surface area $A=24 r^{2}$, which is the derivative of the volume, $V=8 r^{3}$.

Zero Waste by Nick Sayers

By Christian Lawson-Perfect. Posted September 26, 2012

Get ready to smile!

[youtube url=http://www.youtube.com/watch?v=x7Xq4OX7beU]

via Elin Roberts on Twitter

Knitted Spiky Icosahedron

By Katie Steckles. Posted August 20, 2012

As an avid knitter, and mathematician, the birth of a small human in my family inspired me to create a mathematical toy for the tiny person to enjoy while learning about shapes. With my favourite platonic solid being the icosahedron, it was the obvious choice for a knitted toy, and with stellation being all the rage, sticking a point on each face was the obvious next step, especially when it’s such a convenient thing for tiny inexperienced hands to grasp.

PRISMATICA by Kit Webster

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