---The Claw of Archimedes: I designed this weapon to defend the city of Syracuse. The claw was a crane-like arm from which a gigantic large grappling hook was suspended. The claw would drop onto the enemy ships then the arm would swing up, lifting the ship out of the water and sometimes sinking it.
--- Pie: I used the method of exhaustion to approximate and extremely accurate value of pie which is between 3.1429 - 3.1408.
---Sphere and Cylinder: I proved that the volume and surface area of the sphere is 2/3rds of that of a cylinder, including its bases. This is one of my favorite mathamatical proofs and and probably one of the greatest achievements I have ever done.
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