The Pythagorean theorem states:. The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle. This theorem is an extremely useful tool that provides the basis for more complex trigonometry theories such as the converse of the Pythagorean theorem. This theorem, however, isn't a generalization about all triangles.
The Pythagoras theorem doesn't apply to obtuse or isosceles triangles that don't contain right angles. To use the site, please enable JavaScript in your browser and reload the page. Enable contrast version. For a compilation of more proofs than you can shake a stick out, check out Cut the Knot.
The proof she refers to from November is here. We also touched a little bit on the history of the theorem. The relationship between the sides of right triangles was known to many ancient cultures, including Navajo as Henry Fowler told us on a previous episode of the podcast , Babylonian I wrote about Plimpton , a table of Pythagorean triples from around BCE , Chinese, and Indian.
You can read her post and marvel at how clever her student was here. You can learn more about the history of that theorem here and here. Vi Hart has an entertaining video on the topic. For a more staid take on the Pythagoreans , you can start here. In each episode of the podcast, we ask our guest to pair their theorem with something. Nguyen picked one of her great loves: football. Specifically, check out this magnificent hypotenuse run by Ben Watson , which thwarted Champ Bailey's attempted yard touchdown after interception.
You can find Ms. Nguyen at her website , where she shares beautiful writing about teaching, and on Twitter. You can find more information about the mathematicians and theorems featured in this podcast, along with other delightful mathematical treats, at kpknudson.
If you know the height of the roof and the length for it to cover, you can use the Pythagorean Theorem to find the diagonal length of the roof's slope. You can use this information to cut properly sized beams to support the roof, or calculate the area of the roof that you would need to shingle. The Pythagorean Theorem is also used in construction to make sure buildings are square.
A triangle whose side lengths correspond with the Pythagorean Theorem — such as a 3 foot by 4 foot by 5 foot triangle — will always be a right triangle. When laying out a foundation, or constructing a square corner between two walls, construction workers will set out a triangle from three strings that correspond with these lengths.
If the string lengths were measured correctly, the corner opposite the triangle's hypotenuse will be a right angle, so the builders will know they are constructing their walls or foundations on the right lines. The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. For instance, if you are at sea and navigating to a point that is miles north and miles west, you can use the theorem to find the distance from your ship to that point and calculate how many degrees to the west of north you would need to follow to reach that point.
The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal. The same principles can be used for air navigation. For instance, a plane can use its height above the ground and its distance from the destination airport to find the correct place to begin a descent to that airport.
0コメント