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# geometry

## Latest Articles

### In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.

### A Brief History of Tricky Mathematical Tiling

The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.

### Biophysicists Uncover Powerful Symmetries in Living Tissue

After identifying interlocking symmetries in mammalian cells, scientists can describe some tissues as liquid crystals — an observation that lays the groundwork for a fluid-dynamic theory of how tissues move.

### The Mathematician Who Sculpted the Shape of Space

Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.

### Echoes of Electromagnetism Found in Number Theory

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

### How Simple Math Moves the Needle

The spatial intuition behind a three-point turn offers an on-ramp to a century-old geometry problem.

### Mathematicians Cross the Line to Get to the Point

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

### Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

### A Tower of Conjectures That Rests Upon a Needle

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.