Guess what the area is 🤔

Everything reminds me of her.

Toán học đẹp thật

6Rpi minus twice the original given area (2pi•r or pi•d), just as one proves by inverting half the length one side an equilateral triangle backwards geometrically similarly true for an area of 6R minus one times the given area similar - the reason acute-verticed shapes need not be removing area as at high a rate is by the necessity of squaring a unit circle’s radius by a constant coefficient (pi) to interpolate the interior “negative circle”’s area’s removal from the final shape of its tangential radius widening by midpoint inverse square formulaicization as compared to an acute interior n-gon’s such as the equilateral triangular verisimilitude proof by derived accretion integral “area equals the height / 2” squared in unit space on a triangle as a=b=c=(h•.5x)=1 definitionally. Algebraically, unit area of 1 proofing also shows a square area (the other acute interior n-gon aka polygon aka shape) transform to “six times one half” “minus one” exactly when a corner rotates to maximize the area removed from a shape rolling in a complete pinwheeling cutout, as’d show 2 shaded out of 3 from shaded plus 1 unshaded, which is similar math to a circle’s tangent getting circles by a circle with a radius which adds its midlength’s inverse square to itself. Fun and clean exercise if original area of any equilateral non-obtuse vertexed / verticed polygon is equal to 1 with all examples abstracting equilateral unit shape implications given non-obtuse midsection constant relations (poor penta+gons). Proving this common ground between a circle and non-obtuse equilaterals is fun, but showing how many more sections you need for even 2D calculating differently degreed unit shapes by the same simplifications / lack thereof for obtuse angle-including polygons reveals that much more complexity to automation.

Pi * (1.5r) ** 2

pr^2

R/2

I fed this clip to @grok and asked it to redraw this with r=R/2. Stunning, I mean wow!

What's the name of that app that can made this type of diagrams?