... the original or given triangle. This leads to Euclid's mathematical assertion that ˜if in a right-angled triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another' [Proposition 8, Book 6]. Similarity between figures enables one to make comparisons utilizing proportionality. The following are pertinent propositions ... is equal to the two interior and opposite angles and the three interior angles of the triangle are equal to two right angles. (180 degrees) Proposition 4, Book 6: In equia...

• Word Count: 952
• Approx Pages: 4

... famous theorem, it is quite possible that his most lavish accomplishment is the mathematical basis of musical intervals. Pythagoras's theorem which states that the square of the hypotenuse of a right triangles is equal the sum of the squares of the other two sides was actually said to be thought of by Babylonian mathematicians from earlier times. Plato was very found of ... of geometric principles. Not much is known about what advances in geometry were made between the times of Thales and the Pythagoreans. The Pythagoreans advanced the understanding of not only triangles, but a number o...

• Word Count: 750
• Approx Pages: 3
• Grade Level: High School

... named after its first observer, Pythagoras, but it was Euclid's insight what made it clear enough to become the basis for a great number of further mathematical discoveries. "In right-angled triangles-, the Alexandrian mathematician tells us, "the square on the side subtending the right angle is equal to the squares on the sides containing the right angle-. We set out on ... ...

• Word Count: 1043
• Approx Pages: 4
• Grade Level: Undergraduate