See Image Even though our author discusses the \"prevailing tension\" between th
ID: 2984272 • Letter: S
Question
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Even though our author discusses the "prevailing tension" between the algebraic and geometric, we have seen many examples of mathematics relating and connecting algebraic and geometric ideas. In each of the following cases, provide at least one specific example from the history of mathematics as an illustration. The formulas for the areas of various types of polygons can be obtained by geometric dissection. Algebraic formulas can be derived from geometric diagrams. Good numerical approximations to the number pi can be found by geometric reasoning.Explanation / Answer
a. Euler discovered various formulae and theorems for dividing a large control volume/area into multiple set of shapes and finding out their volumes/areas/flow rates using basic summation (which is basic algebra)
b. Pythagoras Theorem, discovered by the great Pythagoras is one typical example of where you can represent a right angled triangle by a simple algebraic formula of a^2=b^2+c^2.
c. That comes from the derivation of the well-known shape circle. Many great mathematicians have defined "pi" as the area of a circle of unit radius.