The human visual system exhibits a remarkable ability to decipher the three-dimensional structure of the world from two-dimensional retinal images. Central to this process is the utilisation of shape ...

Researchers learn to predict how crystals take shape from their internal chemistry, even when the crystal lacks symmetry. A crystal's shape is determined by its inherent chemistry, a characteristic ...

Reflective symmetry is when a shape can be folded in half, with either side of the fold being a mirror image of the other. Rotational symmetry is when a shape can be rotated and it still looks the ...

This course explores some visual aspects of mathematics. Topics are chosen from areas such as geometric constructions, tessellations of the plane, symmetry groups, Platonic and Archimedean solids, ...

2025 marked a historic year in mathematics. Researchers solved a major case of Hilbert’s ambitious sixth problem, proved a sweeping new theorem about hyperbolic surfaces, and settled the longstanding ...

Miriam Rossi, a professor of chemistry at Vassar College, offers the following reply: Snowflakes are symmetrical because they reflect the internal order of the water molecules as they arrange ...

Julia Collins does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...