geometry: Why are squares used to measure areas? etc.

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lisamaths

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Sep 5, 2007
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1) Why are squares chosen as the unit to measure areas? Could other shapes be used? Why/why not? If yes, why do you think mathematicians chose to use squares?

2) How can we choose the size of the “grid" to compute the area of a given figure? Does it really matter what this size is?
 
I don't know that there is a "right" answer to these, only intelligent thoughts and reasoning (plus some research into historicity).

"Could" other shapes be used to measure area? Sure; why not? But how useful would those other shapes be, especially considering how one customarily (that is, historically) measures the simplest shapes? Did "mathematicians" even do the choosing? (I rather doubt it. Mensuration was fairly well established back in ancient Egypt, when "math", such as it was, was still a religious pursuit. The profession of mathematician didn't arise until millenia later, at least in any recognizable form.)

As for choosing grids, isn't that just a matter of choice? Granted, some choices are probably better than others, for a given application, but there is generally more than just one useful choice.

In any case, this question is asking for your thoughts, so... do some thinking! :D

Eliz.
 
lisamaths said:
i am doing it
Click to expand...

Let us know - after you did done it.

Actually to measure the area of an odd shape - generally the area will be divided up into triangles. Other suitable shapes (like circles) have also been used.

About the grid size - one engineering rule of thumb is to have at least ten units within the area of interest. Absolute minimum is - the grid area must be smaller than the area of interest.
 
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