The Impossible is Possible! Squaring the Circle and Doubling the Cube in Space-Time

Authors: Espen Gaarder Haug

Squaring the Circle is a famous geometry problem going all the way back to the ancient Greeks. It is the great quest of constructing a square with the same area as a circle using a compass and straightedge in a finite number of steps. Since it was proven that π was a transcendental number in 1882, the task of Squaring the Circle has been considered impossible. Here, we will show it is possible to Square the Circle in space-time. It is not possible to Square the Circle in Euclidean space alone, but it is fully possible in space-time, and after all we live in a world with not only space, but also time. By drawing the circle from one reference frame and drawing the square from another reference frame, we can indeed Square the Circle. By taking into account space-time rather than just space the Impossible is possible! However, it is not enough simply to understand math in order to Square the Circle, one must understand some “basic” space-time physics as well. As a bonus we have added a solution to the impossibility of Doubling the Cube. As a double bonus we also have also Boxed the Sphere! As one will see, one can claim we simply have bent the rules and moved a problem from one place to another. One of the main essences of this paper is that we can move challenging space problems out from space and into time, and vice versa.

Comments: 18 Pages.

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Submission history

[v1] 2016-02-19 06:49:44
[v2] 2016-02-22 17:51:04
[v3] 2016-02-24 04:24:44
[v4] 2016-03-08 16:32:26
[v5] 2018-12-08 10:50:57

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