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Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.
This is a category for any video game where the player controls actions taking place, at least partially, on Mars. The action must take place on the surface Mars itself, not simply in orbit above Mars. This includes any alternate universe Mars, such as after terraforming, or on a seemingly fantasical Mars, as long as it is in relation to Earth.
It would feature different space agencies that would be either rivals or allies, and the focus would be on the search for extraterrestrial life. [6] Planetary scientist Konstantin Batygin joined the design team to provide feedback on the details of the real-life search for life on Mars, to ensure that the game stays as accurate as possible. [7]
For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...
English: Animated visual proof of Ptolemy's theorem, based on W. Derrick, J. Herstein (2012) Proof Without Words: Ptolemy's Theorem, The College Mathematics Journal, v 43, n 5, p 386 Date 22 May 2022
Per Aspera was announced in June 2019 at the PC Gaming Show. [3] An expansion pack, Green Mars, was released on October 21, 2021. [4] A second expansion, Blue Mars, was released on May 2, 2022. [5]
Lifeless Planet is a 2014 puzzle adventure developed by independent American company Stage 2 Studios and published by Serenity Forge. The game was released on June 6, 2014 for Microsoft Windows and on June 23, 2014 for OS X, and has been ported to the Xbox One on May 13, 2015, Linux on March 25, 2016 and to the PlayStation 4 on July 19, 2016.
Mars After Midnight is a 2024 management video game developed and published by Lucas Pope. [1] The player controls an alien running late-night community support groups on off-colony Mars. The game launched in March 2024 as a Playdate exclusive.