Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY ...

In March, a group of mathematicians identified a thirteen-sided shape called “the hat” that can tile a surface without any patterns repeating. Now the researchers are updating the shape to maintain ...

Fibonacci number patterns and triangular patterns with intrinsic defects occur frequently on nonplanar surfaces in nature, particularly in plants. By controlling the ...

Neurons come in an astounding assortment of shapes and sizes, forming a thick inter-connected jungle of cells. Now, neuroscientists have found that there is a simple pattern that describes the ...

About a year ago, the theoretical chemist Salvatore Torquato met with the number theorist Matthew de Courcy-Ireland to explain that he had done something highly unorthodox with prime numbers, those ...

1. A trade-off between the investments in functional and support structures is a major determinant of leaf physiological activities. A variety of leaf shapes and venation densities occur in coexisting ...

Optical illusions test the limits of human vision by deceiving our eyes and brain. A black-and-white spiral pattern hides a ...