Zoom demo (experimental)

The buttons and pinches off the scale use this page's zoom; the corner buttons stay put while the content grows.

A balance with x + 3 on the left and 7 on the right, a number line under the beam, and a 3-4-5 right triangle on a grid 10987654321012345678910 pivot (0) x 3 7 left pan: x + 3 right pan: 7 x + 3 = 7, so x = 4 take 3 from each pan and the beam stays level a = 4 b = 3 c = 5 3² + 4² = 9 + 16 = 25 = 5² each grid square is 1 by 1

A balance stays level when both pans hold the same amount. On the left are a mystery weight x and a 3; on the right is a 7. Taking the same amount off both pans keeps the beam level, so taking 3 from each side leaves x on the left and 4 on the right.

The numbers under the beam count steps out from the pivot. A weight farther from the pivot turns the beam harder, which is how a steelyard weighs with one small poise.

The triangle on the grid has legs of 3 and 4 squares. Squares built on its sides have areas 9, 16 and 25, and 9 + 16 = 25: the Pythagorean rule, drawn small enough that you need to zoom in to read it.

Try it: pinch anywhere on the page, or use − + Fit in the corner. Zoomed in, drag with one finger to pan. The header and the buttons stay the same size.