Math CentralQuandaries & Queries


Question from Chandler, a student:

I am doing ratios and I was wondering if... well let me explain first. I have data on the arm span and heights of 10 students including myself now i have my measurements of me are 66inches arm span. and 66 inches height. my second piece of data is 71 inches arm span and 67 inches height now my ratio is 71:67 right? i thought i would need to simplify. but i cant really simplify this ratio and these numbers. what do I do?

Hi Chandler.

You have ten sets of data (each "set" is a span measurement and a height measurement), so if you like, you can create 10 ratios, one for every set.

For you, the ratio is 66:66 which you can simplify to 1:1.

For your second piece of data, you have 71:67 (always make the ratio in the same order; here we are using arm span:height, so we should always have the arm span before the height).

Remember that ratios are also fractions and fractions are also decimals. So although 71:67 = 71/67, you are right that this doesn't "simplify". However, by doing the long division (or using a calculator), you can find that this ratio is also about equal to the decimal 1.06.

Another thing you can do with all your data is find an average for the ratios. An easy way to do this is to add up all the arm spans of all ten people and compare that to the average height of all ten people.

Another interesting thing you can do is look for the extreme cases. That is, who has the longest arms in proportion to his or her body? (This would be the largest decimal number) Who has the shortest arms in proportion to the body?

The relationship between arm span and height was first written by a Roman architect about 2000 years ago named Vitruvius (you can Google for that name to learn more). He also looked at other ratios on the human body, such as the width of a man's palm is the width of four fingers and the height of the head (top to chin) is 1/8 of the man's height. In fact, there are many proportions he wrote about that are very useful in figure drawing and art. Leonardo da Vinci drew a man using these proportions, which he called "Vitruvian Man", and this is a very famous drawing that you may have seen before. Here's a link to it.

Stephen La Rocque.

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