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!
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.
Infinite flavor in a finite fruit pastry space!
Further reading: http://www.ams.org/publicoutreach/feature-column/fcarc-circle-limit