Comments by "John Berry" (@user-ud6ui7zt3r) on "2000 years unsolved: Why is doubling cubes and squaring circles impossible?" video.

For accomplishing squaring a circle, you need the following multiplier... 0.88622692545275801364908374167057 . Multiply the length of the diameter of the initial circle by the multiplier... 0.88622692545275801364908374167057 ...to yield the length of a side of a square that will exhibit the same area as the initial circle.
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For accomplishing cube doubling, you need the following multiplier... 1.2599210498948731647672106072782 . Multiply the above number by the length of a side of your original cube, adopt the result as the length of the sides of a NEW cube, and the new cube will have double the volume of the original cube. So, the challenge would be to find a way, using only Ruler and Compass, to create lengths that are... 1.2599210498948731647672106072782 ...times initial linear SIDE lengths. note: It seems reasonable that a person could compute 1.2599210498948731647672106072782 times the length of a side of a cube. Next, a person could set the width of a compass span to equal this result, followed by drawing a circle. Note that the compass span width could be checked against the markings on the ruler. Next, a person could draw a straight line through the center of the circle, by using a ruler. Next, a person could draw another straight line through the center of the circle, but this time, orthogonal to the first straight line. Tangential to where these straight lines meet with the edge of the circle, draw two more straight lines, one horizontal, the other vertical. The four straight lines should now form a square. Use the resulting square as the sides of a cube, and the resulting cube will have double the volume of the initial cube.
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@matiasgarciacasas558 • travel to a sandy beach; • use the compass as a fan; • in the sand, using the ruler, write the necessary multiplication
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@matiasgarciacasas558 My offered conversion factor is merely an approximation to the actual conversion factor. The actual conversion factor should be an irrational number. Also, try using a compass that doesn’t feature a large, internal void.
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@matiasgarciacasas558 Well, I will eventually reply with my method, but first, I’ll give you an opportunity to derive the method, yourself. Also, I find the compass serves adequately as a fan if you leave the compass in the original blister-pak packaging.
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@matiasgarciacasas558 Yeah, you’re right. But what I like to make note of is that pi is not the only noteworthy irrational constant in geometry. The conversion factor that I presented, if memorized, is also very useful.
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