Talk:Squaring the circle

I have removed the nonsense about cylinders. Even if one could manipulate solid objects in Euclidean plane geometry (you can't, obviously), the the issue seems to have been to create a square (the cylinder viewed from its side) from the circle which is its base, or vice-versa, so that the side of the square matches the diameter of the circle. That's trivial—they are the same distance. The problem of "squaring the circle" was to match areas, not lengths. That is, make a square with the same area as the circle.

The 6-step "solution" that was given in the previous version involved manipulating 3-dimensional objects (you can't; this is plane geometry), "unrolling" the side of the cylinder (you can't), folding the resulting sheet (you can't do that, though you can get the equivalent effect with compass and straightedge, but you can't call it "folding"), and so on.

Even as a "joke", this falls flat.

SamHB (talk) 13:30, 2 July 2019 (EDT)

Why do you assume a priori that the area sought is Euclidean plane geometry only. Why? The problem proposes determining the equal area which a three-dimensional object does possess of necessity, since it occupies space with length and width and height. And yes, the area of the surface of a solid can be virtually "flattened" to determine the necessary volume of a container for the solid, a boundary for an enclosed space, as in a problem in architectural engineering and construction. It is enough for me that this discussion take place on the talk page. That is the essence of peer review. I sense from the tone of your response that you are unfamiliar with boolean algebra and logic and the hyper geometries of multidimensional mathematical spaces. With all due and well-wishing respect I suspect your response is subconsciously motivated by an unintentional form of mathematical and philosophical xenophobia. Scientific prejudice is not unknown in debates over hypotheses. The "seven deadly words of committee" before rejection of a proposal are "we have never done it that way before". Think of the advances in human knowledge and potential discovery that were delayed in this way.
Although I proposed a "solution" to the problem lightheartedly, it cannot be demonstrated to be either irrational or unreasonable. I did not propose the solution as a laughable joke, but as a form of legitimate mathematical amusement, as so many mathematical puzzles and novel solutions are by their nature, and they are not mockeries of mathematical reasoning. I did say that no one takes such a solution seriously. Paradoxes have been proposed as entertainment and as serious problems at one and the same time. Challenges make many astute and competent intellectuals smile with enjoyment, and sometimes chuckle with delight, even as they seriously take up the problem proposed. Sometimes what seems insoluble is resolved when someone with sudden insight says, "Let's look at this from a different angle. Maybe we are coming at this from the wrong direction. What if instead of what we normally do, we turn the problem on its head and_____?" Remember how Archimedes shouted, "Eureka!" in solving the problem of determining specific gravity by displacement of water volume and the weight of the whole by disregarding the traditional means of measurement. Your assumption that a Euclidean plane area solution cannot be obtained by the measurement of a third-dimensional cylindrical simple solid over its whole surface area is not only untrue, but ipso facto dismisses unexamined and untried a reasonable solution to the problem which is demonstrably simple. Semper fi --Dataclarifier (talk) 19:23, 11 July 2019 (EDT)