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A three-foot-tall robot named Bumi is about to shake up the humanoid market with a price tag that sounds more like a laptop than a walking, dancing machine. Beijing startup Noetix Robotics has unveiled what it calls the world's cheapest humanoid robot at just $1,370. That's a fraction of what most bipedal robots cost. While competitors like Tesla's Optimus run two to three times higher, and Boston Dynamics' Atlas...

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Random spherical coordinates

Generating random points on a sphere typically involves creating Cartesian coordinates then converting to spherical form, but a more direct approach generates spherical coordinates immediately. While the radius equals 1 and...