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patterns

Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"
geometry

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

Art for "The Universal Pattern Popping Up in Math, Physics and Biology"
Multimedia

The Universal Pattern Popping Up in Math, Physics and Biology

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

Art for "A Math Theory for Why People Hallucinate"
neuroscience

A Math Theory for Why People Hallucinate

Psychedelic drugs can trigger characteristic hallucinations, which have long been thought to hold clues about the brain’s circuitry. After nearly a century of study, a possible explanation is crystallizing.

Crystal diffraction art for "A Chemist Shines Light on a Surprising Prime Number Pattern"
prime numbers

A Chemist Shines Light on a Surprising Prime Number Pattern

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

Illustration of pentagon tiling
Quantized Academy

The (Math) Problem With Pentagons

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

Marjorie Rice
Abstractions blog

Marjorie Rice’s Secret Pentagons

A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.

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.

Bongard puzzle stars
insights puzzle

Solution: ‘Bongard Problems and Scientific Discovery’

Like scientific puzzles, Bongard problems can lead you through a frustrating blind search until you find that simple, elegant rule that fits a seemingly random pattern.

Bongard stars
insights puzzle

Bongard Problems and Scientific Discovery

For your frustration, joy and entertainment, our puzzle challenges you to find general patterns or rules based on seemingly random, specific examples.