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D13. The Experbola
Posted: 2023-05-01 13:40:34In Dilemma 8, we investigated a curve similar to an ellipse, but changing addition to multiplication in its definition. This time, PMP participant William Keehn proposes a similar exploration related to the hyperbola, another conic section, which can be thought of as all of the points ( x , y ) in the plane where…
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D12. Strange Coincidence
Posted: 2023-05-01 13:26:06Let’s listen in on a conversation between siblings divided by math, so to speak: “That’s amazing!” said Mathophila. “The squares of three consecutive positive whole numbers add up to the same number as the squares of the next two numbers.” “Oh, no big deal, that must happen all the time,” replied her brother, Innumeratus. “I…
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D11. Octosection
Posted: 2023-05-01 13:09:45Square A B C D in Figure 1 has been dissected into eight equal-area rectangles. The width of the rectangle shaded red in Figure 1 is 35 units. What is the area of square A B C D ? For a bonus challenge, can you devise and solve a similar problem that dissects a square…
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D10. Half-and-half Hanoi
Posted: 2023-05-01 13:00:28You may be familiar with the Tower of Hanoi puzzle in which you start with eight discs stacked on one of three pegs, each disc smaller than the one below it. The other two pegs are empty. The goal of the puzzle is to move the entire stack of discs to a different peg, according…