Math CentralQuandaries & Queries


Question from Laura, a student:

I am currently working on a math summative in which I have to choose a real life subject and relate it back to the material in my grade 12 math class. I find the history and discovery behind the Pythagorean Theorem and Identity very interesting, but I have yet to find a real-life application of the equations. Yes, I know they are used for finding distances, heights etc., but realistically, how many people actually use it in those situations? Very few. I was hoping for a new application. Is the pythagorean theorem (sin^2x + cos^2x = 1) even applicable? Thank you,

Hi Laura,

Go to the Quandaries and Queries page on Math Central and use the Quick Search to search for the phrase Pythagoras real life. You will receive a list containing some questions we have been asked about out-of-school problems that involve Pythagoras Theorem. In particular look at Penny's response to Tiffany who asked a question similar to yours in 2004. As Penny says "These are not 'made up' school problems but real problems that have arisen in their work or home lives." The list returned from the keyword search also contains some further examples since 2004.

I want to mention one further application and this involves the distance between two points in 3-space. The formula for this distance results from two applications of Pythagoras Theorem. The particular application I want to mention concerns global positioning. In the section of Math Central called Math Beyond School there is a note on navigation. In that note look at the section titled GPS and Circles. The procedure described there involves finding the intersection of three spheres. This means solving three equations, each of which is a distance expression in 3-space that comes from two applications of Pythagoras Theorem .


In May of 2008 the following message came in the Quandaries and Queries mail.

This is not a question but more of another use for what I consider one of the three greatest achievements to the geometric world. I went to college to be a civil engineer but ended up being a sheet metal worker. In my daily work life I use the pythagoras theorem at least 50 times a day. You can literally layout and fabricate some of the most complicated duct work fittings using it, ratios of similar triangles, and a little trigonometry. Fittings such as square to rounds and tapered cones laid out on a pitch are made entirely by using pythagoras theorem. To all those who doubt what there teachers are teaching in class, simple formulas like this one have astounding applications as long as one is able to think out side of the box.



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