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For some reason, the one I have the most trouble intuitively grasping is "Two 12 Inch Pizzas have less Pizza than one 18 inch pizza."
by Ansil849 5y ago
For some reason, the one I have the most trouble intuitively grasping is "Two 12 Inch Pizzas have less Pizza than one 18 inch pizza."
- guerrilla 5y agoThe area enclosed by a circle is πr^2 while 12 and 18 are the diameters, right? The radius of a disc is half the diameter, so 6 and 9, respectively. 2π6^2 < 1π9^2 ~~ 226.2 < 254.5. In other words the area is proportional to the square of the radius, not linearly proportional to the diameter in any way.
- Ansil849 5y ago> In other words the area is proportional to the square of the radius, not linearly proportional to the diameter in any way. Awesome, thanks for that geometry refresher, that makes sense now of course :).
- caf 5y agoSimilarly, if the toppings are distributed evenly across the pizza, the average distance of a piece of topping from the edge is one third of the radius: most of the pizza is near the edge.
- 77pt77 5y ago18/12 = 1.5 > sqrt(2) = 1.4..
- Viliam1234 5y agoTo make it simpler, let's assume that the shape of pizza is a square, i.e. we are talking about a 12×12 inch pizza and a 18×18 inch pizza. This increases the size of both pizzas by the same ratio, so it shouldn't change the answer to "are two small pizzas smaller than one large pizza?". Now let's measure the size in a new unit which is 6 inch long. So the small pizza is 2×2 units, and the large pizza is 3×3 units. twice 2×2 = twice 4 = 8 3×3 = 9