Question

Use the following information.

The Greek mathematician Pythagoras believed that all things could be described by numbers. By “number” he meant positive integers.

Explain why Pythagoras could not find a “number” to describe the value of c.

Short answer

“Number” could not describe $c$ because it is not a positive integer.

Step-by-step solution

- Meaning of “number”

From given information “number” is a positive integer which means it is a natural number.

- Value of c using formula given in question 41

Evaluate c using formula given in question 41 is

$c=\sqrt{2s^2}$

Substitute 1 for s in given formula

$c=\sqrt{2{\left(1\right)}^2}$

- Simplify 212

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

$\begin{array}{c}c=\sqrt{2{\left(1\right)}^2}\\ =\sqrt{2\left(1\right)}\\ =\sqrt{2}\end{array}$

As $\sqrt{2}$lies between natural number 1 and 2 so it cannot be simplified further.

Thus, c is not the “number” defined in given information.