Solve for the perfect omelette with this eggcellent formula!

In fact, if you graph x2 + y2 = 2y, you will obtain a flawless egg shape:

However, there are also other methods to create a perfect ovoid shape using a compass and ruler, as illustrated below.

Typical Ovoids: a – Cundry & Rollet ovoid (1989); b – Classic ovoid; c – Ovoid Sqrt 327 (Dixon, 1987); d – Antonio Castilla ovoid (Cuarado, 2010).

Lateral Mathematics

High math skills are required to solve this puzzle…
Fill in the three boxes below using any of the following numbers: 1, 3, 5, 7, 9, 11, 13, 15.
You are allowed to repeat the numbers.

show solution

The Geometry of the Bees

When constructing a honeycomb, bees aim to minimize wax usage and honey consumption, using the least wax necessary for a comb with maximum honey storage. The wax cells are designed with interlocking opposing layers, sharing facets at closed ends while having open ends facing outwards (see fig. 1). Each cell is a ten-sided structure with a rhombic decahedron form – a hexagonal prism with three rhombi at its closed end (fig. 2). Mathematicians have extensively studied the highly efficient isoperimetric properties of these cells. The question remains: What angle alpha maximizes volume while minimizing surface area on each cell face when the hexagonal prism’s faces have a width of 1 unit?

Continue reading “The Geometry of the Bees”