This art is geometry "the measuring of Earth. ... In thirteen books he collected The Elements of geometry, starting from the most basic concepts, "a point is that which has no part- and "a line is breadthless length-. ... In a rigorous, fast, and easily understandable way, XLVII proves that in a right-angled triangle the square of the hypotenuse, or diagonal, is equal to the sum of the squares on the remaining sides. This theorem is 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 mat...

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

His interest in mathematics is said to have began from when he observed a solar eclipse on October 18, 320 and then since has focused his work on geometry. ... The purpose of the volumes were to revive geometry and restore it to a level of significance, usually by providing further explanations or supplements to the works of previous geometers. ... Book IV is an extension of Pythagoras" theorem for parallelograms constructed on the legs of any triangle. ... Pappus formulated the volume of a solid of revolution, which was later called The Pappus - Guldin theorem. ... His theorem was that the v...

• Word Count: 647
• Approx Pages: 3
• Grade Level: Undergraduate

Basic arithmetic and geometry formed the basis of what the mathematical world had to offer at its very beginnings. ... This theory incorporates the idea that musical sounds have mathematical tones of energy which ultimately allow them to relate with patterns of proportion dealing with angles, shapes, and movements. ... As mentioned in the Stanford Encyclopedia, "Pythagoras is said to have transformed the philosophy of geometry into a form of liberal education, to have investigated its theorems in an immaterial and intellectual way and specifically to have discovered the study of irrationa...

• Word Count: 1076
• Approx Pages: 4
• Grade Level: Undergraduate

In the 12th century, the Indian mathematician Bhaskara II developed an early derivative representing infinitesimal change, and he described an early form of "Rolle's theorem". ... James Gregory proved a special case of the second fundamental theorem of calculus in AD 1668.       ... The basic insight that both Newton and Leibniz had was the fundamental theorem of calculus.       ... Modern differential calculus on mean value theorem Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. ...

• Word Count: 6149
• Approx Pages: 25
• Grade Level: Undergraduate