• The ancient question of whether or not it’s possible to construct a circle with the same area as a given square using only a drawing compass and straightedge was finally answered in 1882, where it was proved that pi is a transcendental number, meaning it cannot be accurately represented in a compass-and-straightedge system. • This inability to accurately represent pi is just one of the ways in which these systems resemble a computer, a similarity that[0x0mer] explored in CasNum. • The core of the program represents operations with a drawing compass and unmarked straightedge. • There are only a few operations that can be used for calculation: constructing a line through two points, constructing a circle centered at one point and intersecting another point, and constructing the intersection(s) of two lines, a line and a circle, or two circles. • An optional viewer visualizes these operations. • Another class builds on top of this basic environment to perform arithmetic and logical operations, representing numbers as points in the Cartesian plane.

Article Summaries:

  • The ancient question of whether or not it’s possible to construct a circle with the same area as a given square using only a drawing compass and straightedge was finally answered in 1882, where it was proved that pi is a transcendental number, meaning it cannot be accurately represented in a compass-and-straightedge system. This inability to accurately represent pi is just one of the ways in which these systems resemble a computer, a similarity that [0x0mer] explored in CasNum. The core of the program represents operations with a drawing compass and unmarked straightedge. There are only a few

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