At an American Mathematical Society meeting, high school students presented a proof of the Pythagorean theorem that used trigonometry—an approach that some once considered impossible
The Pythagorean theorem lets you calculate the longer side of a right triangle by summing the squares of the other two sides.Calcea Johnson and Ne’Kiya Jackson, both at St. Mary’s Academy in New Orleans, announced their achievement last month at an American Mathematical Society meeting. “It’s an unparalleled feeling, honestly, because there’s just nothing like it, being able to do something that ...
The Pythagorean theorem provides an equation to calculate the longer side of a right triangle by summing the squares of the other two sides. It is often phrased asrepresent the lengths of the three sides of a right triangle, a triangle with a 90-degree angle between two of its sides. The quantityis the length of the longest side, called the hypotenuse.
Now measure the angle between the hypotenuse and the table. Mathematicians define the sine of this angle as the height of the vertical side divided by the length of the hypotenuse. The cosine of this angle is the length of the horizontal side divided by the hypotenuse. The Pythagorean theorem is therefore equivalent to the equation sin=1.
But that’s not always true. In their talk at the American Mathematical Society meeting, Jackson and Johnson said a trigonometric identity called the law of sines didn’t depend on the Pythagorean theorem and that they could use it to prove the theorem.among students. “It kind of makes me wish I still had a class so I could talk about it,” he says.
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