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geometry

15 pentagon tessellations
geometry

Pentagon Tiling Proof Solves Century-Old Math Problem

A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.

Abstractions blog

How to Use a Sphere to Talk to Mars

To avoid garbled messages, mathematicians might translate them into geometric form.

Icosahedron
geometry

A New Path to Equal-Angle Lines

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

Illustration: diver searching for new math
Quantized Columns

Quantum Questions Inspire New Math

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

Thomas Royen at his home in Schwalbach am Taunus, Germany.
statistics

A Long-Sought Proof, Found and Almost Lost

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

Mobius strip illustration
Abstractions blog

The Hidden Twist to Making a Möbius Strip

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

geometry

A Fight to Fix Geometry’s Foundations

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

Hyperbolic Crochet
Abstractions blog

How Curvature Makes a Shape a Shape

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.

Julia Set Contest
Abstractions blog

Test Your Mathematical Sculpting Skills

Can you turn a two-dimensional fractal into a 3-D object? Break out your scissors and tape for a chance to win a 3-D printed sculpture.