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A Resource Guide for Philosophy Students

Created by Jennifer Leslie Torgerson, MA

This page last modified:  September 18, 2012

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School of Athens

 

Meno Diagrams

 



 

 

Figure One: 

 

Assume that each small square is 1 unit in length, thus the entire square is 4 x 4.

Squares have 4 equal sides.

 

What is the area of the yellow square?

 

1.

 

What is the area of the yellow/orange square?

 

4 (side length of square is 2).

 

What is the area of the yellow/orange/red square?

 

9 (side length of square is 3).

 

What is the area of the entire diagram?

 

16 (side length of square is 4).

 

So a square with the side length of 4 has an area of 16.

 

*ponder*

 

What length would the side of the square need be for the area to be 8?  Can it be a natural number?  Let’s try a different approach

 

 

Figure Two:

 

Assume that the green square to right is the 4 x 4 square above.  What is the length of the side of the white square?


The white square has an area of 8.

  

      

Using the Pythagorean Theorem, it may be possible to solve the problem:

 

22 + 22 = C2

4 + 4  = C2

8 = C2

Square root of 8 = C

 

The answer cannot be given as a natural number.

 

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