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Chapter 1: Q42. (page 16)

Use the following information.

The Greek mathematician Pythagoras believed that all things could be described by numbers. By 鈥渘umber鈥� he meant positive integers.

Explain why Pythagoras could not find a 鈥渘umber鈥� to describe the value of c.

Short Answer

Expert verified

鈥淣umber鈥� could not describe c because it is not a positive integer.

Step by step solution

01

- Meaning of “number”

From given information 鈥渘umber鈥� is a positive integer which means it is a natural number.

02

- Value of c using formula given in question 41

Evaluate c using formula given in question 41 is

c=2s2

Substitute 1 for s in given formula

c=212

03

- Simplify 212

To evaluate the length of hypotenuse, first evaluate power then perform multiplication and finally simplify square root as shown below.

c=212=21=2

As 2lies between natural number 1 and 2 so it cannot be simplified further.

Thus, c is not the 鈥渘umber鈥� defined in given information.

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