...however. It goes hand in hand with knowledge and is the constantly resounding overtone of every study. 107 "The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two other sides" visually demonstrated. 108 CHAPTER IX The Thirteen-Year-OIds...

...and the descriptive properties, in which such measure is unessentiaL The Pythagorean theorem, that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs, is a metric property. As an example of a descriptive property...

...structure of the triangles. This structure is specified by the Pythagorean theorem, which may be stated, the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. Let us look at a crude presentation of the Pythagorean...

...about AABC. Students will need to be reminded that the Pythagorean relationship not only implies that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides, but conversely, if such a relationship exists among...

...example. I have never heard of any rational person who both understood and rejected the claim that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. But it is hard to think of any arguments for substantive philosophical...

...to an enormous amount of mathematics, can be thought of as a statement about shapes. "The (area of the) square on the hypotenuse of a right triangle is equal to the sum of the (areas of the) squares on the two legs of thnt triangle. " Alternatively, it can be...

...object, say, a sail, which has the shape of a right triangle. The Pythagorean theorem tells us that the square on the hypotenuse of a right triangle is equal to the sum of the squares on its two other sides. By virtue of this theorem, if we know the length of...

...on the path it would follow for twenty centuries. The first was the discovery— and proof— that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. The second was the discovery— and proof— that when...

...ahead of it only the discovery of Pythagoras, which we have also had occasion to use, that the area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two side: C2 = A2 + B2. To understand Einstein's celebrated...

...a good argument, it will not persuade them. person who both understood and rejected the claim that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other sides. But it is hard to think of any arguments for substantive...