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What is an Example of an endpoint in real life?
Death is the ultimate endpoint. End of a race.
How did euclid die?
Little is known about Euclid's death, but most people are sure that he lived from 325 B.C. and died in 265 B.C.
What does buried half length mean?
It means the lower half of the body is buried below ground, while the upper half is left. Usually performed as a means of torture in ancient times. Person was left stranded without food or water which obviously would be a slow and painful death.
What brand has a sphere with lines in its logo?
It's technically a circle rather than a sphere (the highlighting does make it look sort of three-dimensional), but the most famous company I know of that has a logo that could be described in that way is AT&T. If it's on something old, their 1984 "Death Star" logo fits the description even better.
Why were attempts to square the circle and duplicate the cube by simple geometrical methods important to the field of mathematics?
About 2400 BCE the Greeks tried to construct a square that had the same area as a circle, using only a straightedge and compasses. They also tried to construct a cube having twice the volume of a given cube, with the same tools. The failure of these attempts led mathematicians to realise that the cube root of two and the square root of pi are both irrational. Pi is not only irrational, but also transcendental. This is an important difference because the cube root of two can be constructed by geometrical methods that are more complex than just straightedge and compasses, while pi can not be constructed by any geometrical method involving only a finite number of steps. It took more than two thousand years from the death of Hippocrates of Chios (not to be confused with Hippocrates the physician) before mathematicians began to get a real grip on irrational and transcendental numbers. As is so often the case in Mathematics and Science, the long search led to many, many other discoveries along the way.
