Numbers 1 to 32 are placed along the circumference of a circle without repeating any number and still the sum of any two adjacent numbers in this circle is a perfect square!
Six Points on a Circle
Take 6 points on a circle such that every second edge (green chords) has length equal to the radius of the circle. Then the midpoints of the other three sides of the cyclic hexagon form an equilateral triangle.
Read more: https://www.archimedes-lab.org/2-Sunday_puzzle_43.html
Coxeter Disc
Infinite flavor in a finite fruit pastry space!
Further reading: http://www.ams.org/publicoutreach/feature-column/fcarc-circle-limit