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Mistake of Pythagoras is a modification for Half-Life 2, developed only by Koumei Satou, who is also the developer of Sweet Half-Life, a mod for Half-Life.
The modification was made in Hammer and Faceposer without any coding, in nine months.
Gameplay involves telekinesis and many NPCs from Half-Life 2, who are, most of the time, friendly.
The player takes the role of Gordon Freeman in a parallel world. The city is under attack from unknown metallic enemies and the player has to find a way to stop the invasion by traveling into their world and correcting the "mistake".
Gordon Freeman, a scientist in a small town, is called to action when an unstable teleportation event causes large numbers to fall from the sky as well as gigantic, metal, triangular crafts that begin terrorizing the town. After fighting his way through the ruined city, Gordon reaches the teleporter that caused the event and unwittingly gets sent into a parallel dimension. There lies a series of elaborately designed temples (inspired by Claude Ledoux) which house their own teleporter functions which allow Gordon and Barney Calhoun to jump to each building in an attempt to find a way back to their home world. After the final teleporter sequence fails, Gordon is thrust into yet another dimension, while Barney and his soldiers are left to fight the advancing hostiles. Here, he fights against an army of hostile soldiers alongside friendly striders and gunships that allow Gordon to proceed into a mysterious lair, filled with anti-gravitational fields, more flying triangles, and a series of puzzles. After these encounters, Gordon meets up with Alyx Vance who came to rescue him with the help of a group of citizen soldiers. They proceed into another temple which hosts a battle between Gordon's forces and one of the hostile, enemy crafts. This is destroyed and Alyx and Gordon come across a teleporter which would allow them to escape from the mysterious world. As they are about to teleport, another of the enemy crafts attacks them, causing Gordon to be thrust into yet another alternate dimension, where he comes across more enemies, and is eventually given the power of psycho/telekinesis by a large white machine, allowing him to affect the environment simply by looking at it, as well as finding another Gravity Gun. After destroying a large gray machine, he is warped into a room filled with floating numbers, and a picture of a white square, with two orange squares on top of it. He eventually figures out how to fix the "mistake" and is sent back to his own universe. As he reunites with Barney and Alyx, the white machine from before appears out of a portal, only to be shot down and destroyed by the unified forces of the Combine, Metrocops, and human forces. In the end, Breen appears and asks what is going on, only to be greeted by the sight of a small band of Striders walking away from a large plot of land filled with flowers, with part of the white machine placed on top as a marker.
The mod received 12th place on the ModDB "Mods of 2005" contest. 
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