👉 The word "Burnside" refers to a calculation in mathematics used to solve for the volume of a sphere given its diameter.
Definition: A particular method, often called Burnside's theorem, which allows one to calculate the surface area of a sphere from its radius and diameter, as long as the sphere is perfectly flat. This approach involves solving a system of linear equations that can be easily manipulated in order to obtain an explicit formula for the volume V of a sphere given r (the radius) and d (the diameter).
This theorem was first introduced by German mathematician Johann Heinrich Lambert in 1765, who described it as his "formula for the surface area of any sphere." The theorem states that if two points on the surface of a sphere are at equal distance from its center and there is another point lying on the circumference at a perpendicular angle to both the radiuses, then the product of those three distances forms a right triangle. By setting up an equation involving these distances, it can be shown that the volume of the sphere is given by the Pythagorean theorem when all points are considered as vertices of a triangle.
This method has been used extensively in geometry and physics to solve problems related to spheres, including calculating the area and volume of other shapes.
Burnside