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The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
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Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
The area within a circle is equal to the radius multiplied by half the circumference, or A = r x C /2 = r x r x π.. Liu Hui argued: "Multiply one side of a hexagon by the radius (of its circumcircle), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the ...
square root scales – setting the cursor to any value on R1 or R2, find (area of a circle of radius ) under the cursor on the DF scale ST, SRT: used for sines and tangents of small angles and degree–radian conversion Sh, Sh1, Sh2: used for finding hyperbolic sines on the C (or D) scale Ch
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To account for other components in a wall such as framing, first calculate the U-value (= 1/R-value) of each component, then the area-weighted average U-value. An average R-value is 1/(average U-value). For example, if 10% of the area is 4 inches of softwood (R-value 5.6) and 90% is 2 inches of silica aerogel (R-value 20), the area-weighted U ...
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