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Given the cube below:

If the cube is to be cut into several tetrahedrons and no other shapes allowed, what is the minimum number of tetrahedrons it can be cut into?

If the cube has a volume of 1000 cubic centimeters, what would be the volume of the largest tetrahedron that can be cut from this cube?



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Bits and Beyond...


Plato (427-347 B.C.) was the son of wealthy and influential Athenian parents.  The original name of this aristocrat was Aristocles, but in his school days he was nicknamed Platon because of his broad shoulders.  He was a student of Socrates.  After the death of Socrates, he went to Italy and studied under the students of Pythagoras.  Here, he also spent several years as an adviser to the ruling family of Syracuse.  In 387 B.C., he returned to Athens and established his school of philosophy, the Academy, where Aristotle was one of his most notable students.  Most of his written works are in the form of dialogues.  These works include The Crito, The Phaedo, The Phaedrus, The Symposium, and The Republic.


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