A right triangle. This is the proof of the Pythagorean Theorem supposedly written by Pythagoras about 500 BC: The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). A2 + B2 = C2. Try it yourself: if Side [...]
An eclipse of the moon. You can see the curved shadow of the Earth. Once people have seen that something happens through observation, sooner or later it will occur to them to ask why it happens. And is there any way to prove that it will happen the same way every time? Sumerians developed advanced math to [...]
This is a right triangle, because one of the angles is a right angle. A right triangle is any triangle where one of the angles is exactly 90 degrees, or a right angle. You can't have more than one 90 degree angle in a triangle, or it would be a rectangle. In a right triangle, the side opposite [...]
This is a rectangle. A rectangle is a flat shape, in one plane. It's defined by four points at the four corners. A rectangle has two sides of equal length opposite each other, and two other sides of equal length opposite each other, and four corners, all right angles (90 degree angles). A square is a special kind of rectangle. [...]
Geometry: This is an equilateral trangle. What is geometry? The simplest geometric idea is the point, and then the line, the plane, and the solid. Shapes like circles, squares, rectangles, and triangles are flat, and we can think of them as being parts of a plane, flat like a drawing. What is a point? What is a plane? From planes to solids All [...]
This is an isosceles triangle. Isosceles triangles have at least two sides that are exactly the same length. This forces two of their angles to also be acute angles of exactly the same size. In this blue triangle, the two longer sides are the same length, which forces the two bottom angles to be the same size. If the [...]
This is an equilateral triangle. What makes a triangle equilateral? Equilateral triangles have all three sides exactly the same length. Because their sides are the same length, the three angles of an equilateral triangle are also all the same size, so they're each one third of 180 degrees, or 60 degrees. What is a triangle? What are angles? All [...]
Near where Pythagoras lived: Doric temple at Paestum, Italy Who was Pythagoras? Pythagoras lived in the 500s BC. He was one of the first Greek mathematical thinkers that we know about, after Thales. Who was Thales? All about Greek mathematics Lots of articles about ancient Greece Pythagoras spent most of his life in the Greek colonies in [...]
Greek mathematics: An Egyptian papyrus from about 100 AD which is a piece of one of Euclid's books Greek math: geometry not algebra Because people in ancient Greece had only very clumsy ways of writing down numbers, they didn't like algebra. Ancient Greek numbers What is algebra? All our ancient Greece articles They found it very hard [...]
Diagram for proving the Pythagorean Theorem You can prove the Pythagorean Theorem for yourself, using the proof described on the Pythagorean Theorem page. Just get a square piece of paper, and draw the lines on it that you see in the third drawing (the drawing of a square). Draw the diagonal lines as in [...]
