How. 81 ISN’T A PERFECT CUBE. HOW THE HELL AM I SUPPOSED TO DO THIS?!

x^3 - 81x = x(x^2 - 81) = x(x - 9)(x + 9)

How. 81 ISN’T A PERFECT CUBE. HOW THE HELL AM I SUPPOSED TO DO THIS?!

x^3 - 81x = x(x^2 - 81) = x(x - 9)(x + 9)

Sperner’s lemmaColor the vertices of a triangulated triangle with three colors such that:

- each vertex of the main triangle has a different color;
- each vertex on an edge of the main triangle is colored with one of the two colors at the end of its edge;
then there exists a small triangle whose vertices are colored with all three different colors. More precisely, there exists an odd number of such triangles.

This result looks playful and innocent but is in fact quite powerful. It is known, for instance, to lead to an easy proof of Brouwer’s fixed point theorem. Its power mainly lies in building bridges between discrete, combinatorial mathematics and continuous mathematics.

(via spring-of-mathematics)

(Fonte: appliedmathemagics)

The field of astrophysics has a stubborn problem and it’s called lithium. The quantities of lithium predicted to have resulted from the Big Bang are not actually present in stars. But the calculations are correct — a fact which has now been confirmed for the first time.

(Fonte: studygeek, via themathkid)