ahmedsalman:

Overview: The Spidron is a planar figure consisting of two alternating sequences of isosceles triangles which, once it is folded along the edges, exhibits extraordinary spatial properties.  The Spidron can be used to construct various space-filling polyhedra and reliefs, while its deformations render it suitable for the construction of finely adjustable dynamic structures.

With details: A spidron is a plane figure consisting of an alternating sequence of equilateral and isosceles (30°, 30°, 120°) triangles. Within the figure, one side of a regular triangle coincides with one of the sides of an isosceles triangle, while another side coincides with the hypotenuse of another, smaller isosceles triangle. The sequence can be repeated any number of times in the direction of the smaller and smaller triangles, and the entire figure is centrally projected through the mid-point of the base of the largest isosceles triangle.

More fantastic info and shapes here.

(Source: inthenoosphere)

curate:

A study of medieval Islamic art has shown some of its geometric patterns use principles established centuries later by modern mathematicians. Researchers in the US have found 15th Century examples that use the concept of quasicrystalline geometry. This indicates intuitive understanding of complex mathematical formulae, even if the artisans had not worked out the underlying theory, the study says.

The research shows an important breakthrough had occurred in Islamic mathematics and design by 1200. ”It’s absolutely stunning,” Harvard’s Peter Lu said in an interview. ”They made tilings that reflect mathematics that were so sophisticated that we didn’t figure it out until the last 20 or 30 years.” BBC NEWS via abbyjean via hierology

(via ayse)

The Tetractys (also known as the decad) is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself — in seedlike form — the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the mysteries of the divine realm. So revered was this ancient symbol that it inspired ancient philosophers to swear by the name of the one who brought this gift to humanity— Pythagoras.

Hat tip: Michael Paukner

Nature by numbers, a short movie.

This is the kind of stuff I would wish our schools are filled with. I bet you half these numbers don’t even make sense to about 85% of viewers. But its not their fault, its the failings of our education system that is to blame.

Hat tip: NPR