William Dunham 's Journey Through Genius

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The author of Journey through Genius, William Dunham, begins this chapter by depicting how mathematics was spurred and developed in early civilizations. Dunham focuses primarily on the works’ and achievements’ of early Egypt, Mesopotamia, and Greece in this section. These ancient societies, as they developed, produced mathematicians such as; Thales, Pythagoras, and Hippocrates, who turned a basic human intuition for space and quantity into applicable everyday mathematics. The primary influences driving the development of early mathematics were the issues of growing civilizations, most notably counting commodities, taxation, and the division of land equally, rather than a pure desire for understanding that is seen in mathematics today. These influences culminated in the development of early arithmetic and geometry. The first civilization that is discussed is early Egypt. Records have been found referring to mathematics done in Egypt showing a rudimentary understanding of the Pythagorean Theorem as it pertains to the construction of triangles with whole number sides before the creation of the Pythagorean Theorem. An example lies in an ancient Egyptian construction of a rope with knots forming 12 evenly spaced segments along the length of the rope. They knew if a triangle having sides of 5, 4, and 3 segments was formed it would form a triangle containing a right angle. However, it is important to state that evidence has not been found that ancient Egyptians understood exactly

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