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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.

Related Questions

Is octagon fundamental region?

No. A fundamental region is usually a circle.


When was Circle Housing Group created?

Circle Housing Group was created in 1968.


What group would a triangle and a circle belong in?

A triangle and a circle would belong to the group of geometric shapes. Both are fundamental figures in geometry, characterized by their distinct properties: a triangle has three sides and three angles, while a circle is defined by its round shape and constant radius from a central point. They can also be classified under two-dimensional figures, as they both exist on a flat plane.


The first and fundamental social group is thought to be the?

family


What makes a circle?

organised a group


What line segment connects to the center and a point on a circle?

The line segment that connects the center of a circle to a point on the circle is called a radius. Every radius of a circle is equal in length, and it is a fundamental element of the circle's geometry. The distance from the center to any point on the circle remains constant, defining the circle's size.


The first and fundamental social group is thought to be?

Dance swimming


What is student quality circle?

student quality circle is the group of 4 to 10 member


The radical group that opposed African American's rights was?

The KKK, short for Ku Klux Klan. Ku Klux means circle and Klan means group. It's a circle of white people who formed a group, and they think black people should not be in this circle.


What is a communication cycle?

the group or organisation in which we comunicate is called as comunication circle for example friend circle.


What is the best definition of a circle -APEX?

A circle is defined as the set of all points in a plane that are equidistant from a fixed point, known as the center. This constant distance is called the radius. The circle is a fundamental shape in geometry, characterized by its roundness and symmetry.


What group of shapes does a circle belong in?

2 dimensional shapes