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How to Flatten a Sphere

In geometrical terms, a sphere is a three-dimensional object in which all points of its surface are exactly the same distance from its central point, meaning that it is perfectly round. Physically, spherically objects cannot usually be flattened completely. There are always some areas that are crumpled or distorted, a problem that mapmakers encounter when rendering globes and the physically round earth flat. In a purely mathematical sense, however, a sphere can be flattened by calculating its surface area and then rendering that area as a flat plane. Since pi, an irrational number, must be used in this calculation, the exact surface area will never be precise.

Instructions

- 1
  Find the radius of the sphere. The radius of the sphere is the distance between its center point and its surface, just like in a circle. If you don't know where the center point it, measure the diameter of the sphere, the distance from one side to another, and divide that value in half.
- 2
  Square the diameter of the sphere. To square a number, multiply it by itself. For example, four squared equals 16, five squared equals 25.
- 3
  Multiply the squared diameter of the sphere by pi. Pi is an irrational number that has no absolute value but continues indeterminately into infinity when rendered numerically. However, it is often rounded to its nearest one-hundredth using the decimal system and rendered as 3.14, an approximation of its true value. For example, multiply 16 (the sphere with the radius of 4) by 3.14, which would equal 12.56.
- 4
  Multiply that value by 4. The full equation for finding the surface value of a sphere is 4 times pi times the radius squared. This equation will help you find the surface area of any sphere, as long as the radius is known. In the example of the sphere with the radius of 4, the total surface area of the sphere is 50.24.
- 5
  Now construct a flat plane with a total surface area equal to or approximating the total surface area of the sphere. You have just flattened a sphere.

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