Why is it when a ballerina stands on her toes she exerts more pressure than an elephant on all fours

I'm not sure that's true ... we'd need to see some numbers.

But if it is true, it's the same reason why some places don't

want ladies to walk on their floors with high heels.

Pressure is (weight) divided by (area).

Pressure exerted

by a ballerina = (ballerina's weight) / (area of her toe on the floor)

Pressure exerted

by an elephant = (elephant's weight) / (area of 4 elephant feet)

Pressure exerted by

a lady in high heels = (lady's weight) / (area of 1 or 2 heels)

You can see that the greatest weight might not exert the greatest

pressure, and the smallest weight might not exert the smallest

pressure. The area is important, and it takes an awful lot of toes

or high heels to equal the area of one or more elephant's feet.