This is a bit of a silly question about a very simple mathematical formula, but I wondered whether some Anons familiar with the history of mathematics knew more about it.The formula in question is Heron's formula.That formula gives the area of a triangle in terms of a square root of a product of FOUR lengths. Now, the conventional wisdom is that the Ancient Greeks had no idea that there could be more than three dimensions; but if they considered the product of four lengths, they had been dealing with the "hypervolume" of some four-dimensional object, albeit only en passant in order to take its square root and find a two-dimensional area.So do you think that the Ancient Greeks had some inkling of higher dimensions? How else could they have even considered the possibility of discovering Heron's formula in the first place otherwise? A product of four length makes no sense unless you accept the idea of higher dimensions.
Because it's geometric, we write herons formula algebraically but Greeks didn't need a 4d, modern algebra smuggles metaphysics into notations
>>16895450Guy, there's a square root on the outside. Square rooting a 4d object gives you 2d, cause area is 2d length x width
A triangle? Or a pyramid?A pyramid is 3 dimensions, a triangle is 2 dimensions.A pyramid can have base 3, base 4, base 5 and so on...Height can vary in accordance with block size availability.
>>16895450not from the history side of the question, but you might enjoy ithttps://www.mi.sanu.ac.rs/vismath/carter2011mart/Carter.pdf
>>16895450Computing the area of a box actually involves 6 lengths: the sides of the unit cube and the sides of the box. How could the Greeks do this if they didn't even know about 6D superconformal field theory?
>>16895740the volume*
