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In a Pythagorean triangle, and all three sides are whole numbers. But there are also three more diagonals on the three surfaces (D, E, and F) and that raises an interesting question: can there be a box where all seven of these lengths are integers?
Fortunately, not all math problems need to be inscrutable. So you're moving into your new apartment, and you're trying to bring your sofa.
Here are five current problems in the field of mathematics that anyone can understand, but nobody has been able to solve. The problem is, the hallway turns and you have to fit your sofa around a corner.
According to the inscribed square hypothesis, every closed loop (specifically every plane simple closed curve) should have an inscribed square, a square where all four corners lie somewhere on the loop.
This has already been solved for a number of other shapes, such as triangles and rectangles.
If it's a small sofa, that might not be a problem, but a really big sofa is sure to get stuck.
If you're a mathematician, you ask yourself: What's the largest sofa you could possibly fit around the corner?
But squares are tricky, and so far a formal proof has eluded mathematicians.
The happy ending problem is so named because it led to the marriage of two mathematicians who worked on it, George Szekeres and Esther Klein.
And they are even, so they could be 2 and 4, or 4 and 6, etc.
We will call the smaller integer n, and so the larger integer must be n 2 And we are told the product (what we get after multiplying) is 168, so we know: n(n 2) = 168 We are being asked for the integers Solve: That is a Quadratic Equation, and there are many ways to solve it.