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What is the fundamental group of a genus g surface?
The fundamental group of a closed orientable surface of genus g is the quotient of the free group on the 2g generators a1,...,ag,b1,...,bg by the normal subgroup generated by the following product of g commutators: a1b1a1-1b1-1...agbgag-1bg-1.
What is Pi R Squared?
The formula for the area of a circle is πr^2, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. So, "pi r squared" refers to the area of a circle, calculated by multiplying π by the square of the radius. This formula is fundamental in geometry and mathematics for finding the area enclosed by a circle.
How many degrees is one eighth of a full circle?
One eighth of a full circle is equal to 45 degrees. A full circle is 360 degrees, so to find one eighth of that, you divide 360 by 8, which equals 45. This is a fundamental concept in geometry and trigonometry, where understanding angles and their measurements is crucial.
Why is pi a part of every circle's formula?
The number pi is a part of every circle's formula because there is a fundamental relationship between the diameter (d), or radius (r), if you prefer, and the circumference (c) of every circle, regardless of its size, and the relationship is expressed in one of two ways: c = pi d c = 2 pi r Both expression say the same thing, and either (both) apply to every circle you can construct in planar space.
What is a 180' circle?
There is no 180' circle that would be half a circle. A complete circle is 360 degrees A circle is 360º no matter what its size is.
