Stage 2 · New Numbers / #10
Ratios: Shapes That Survive the Magnifying Glass
Coming soon
The video is in production. Follow along on GitHub to hear when it is out.
The idea
Multiply the width and the height by the same number and the width is still the same multiple of the height: the ratio, and so the shape, doesn't change. But area is width times height, so each side multiplies once; scale by two and the area goes up four times.
A common mix-up
Scale by two and everything doubles, area included; and adding the same amount to width and height keeps the shape too.
Where it stops working
Add two squares to both the width and the height and 3 : 2 becomes 5 : 4, so the photo gets squarer; scale the sides by two and the area isn't doubled, it's four times as big.
School year
China 6