... of the apparatus of the calculus contributed to the fact that it was his version of the calculus that largely determined the subsequent development of mathematical analysis. In addition to analysis, Leibniz made a number of important discoveries in other fields of mathematics: combinatorics, algebra (the principles of the theory of the determinants), and geometry, where he laid the foundations for the theory of the contiguity of curves (1686), worked out, together with Huygens, the theory of the envelopes of a family of curves (1692-94), and proposed the idea of ... Cauchy, differential...

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

... passing a blacksmith's shop and his ear was caught by the regular intervals of sounds from the anvil. When he discovered that the hammers were of different weights, it occurred to him that the intervals might be related to those weights. Pythagoras was correct. Pythagorean philosophy maintained that all things are numbers. Based on the belief that numbers were the building blocks of everything, Pythagoras began linking numbers and music. Revolutionizing music ... is now known. According to Rowell, Pythagoras began his experiments demonstrating the tones of bells of different sizes. Bell...

• Word Count: 1354
• Approx Pages: 5
• Has Bibliography
• Grade Level: Undergraduate

... a metallic purple sheen. In the previously noted exhibitions, Stella would again push the envelope of 1950s painting by altering the canvases into more unique picture frames. One instance had him producing his flabbergasting stripes on letter-shaped canvases, such as a "T- or a "U- or an "H-. The other exhibition he put on showcased his precious stripes building perimeters around hollowed polygonal shapes, ... he began the drawings for what would become the Polish Village series (1971-73), and, perhaps, by the opportunity to reflect on his development as outlined in his 1970 retrospectiv...

• Word Count: 4097
• Approx Pages: 16
• Has Bibliography
• Grade Level: Undergraduate