... sum of the angles in a triangle are always greater than 180. When most people try and visualize a triangle containing angle sums greater than 180 they say it's impossible. They're right, in Euclidean geometry it is impossible, but as for Spherical geometry, it is possible. Think of the triangle on a sphere, and then try and visualize it. See Appendix 1-1. When thinking ... are contained on the sphere and curve. Although the lines curve, they are still parallel to the sphere in hyperbolic geometry. Even though the lines do have some similarities, there are three theorems in Euclide...

• Word Count: 1671
• Approx Pages: 7
• Has Bibliography

... considered to be the greatest mathematician of antiquity and made his greatest contributions in geometry (Archimedes of Syracuse. math). Archimedes literally invented the study of hydrostatics. In one particular result he was able to compute the maximum angle that a (paraboloid) ship could list before it capsized - and he did ... using combinations of pulleys. Although he had many good mechanical inventions, he enjoyed mathematical theory more. He was often so into his geometry that his servants would force him to get into a bathtub and, even while his servants anointed him with oils an...

• Word Count: 1479
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School