Geometry is in Mathematics.
Culture, General Things, Mathematics, Geometry, Circle
Circle. A circle is an ellipse with equal width and height; a = b.
The ellipse equation when a = b: x2/a2 + y2/a2 = 1 or simplified ( x2 + y2 ) / a2 = 1 or y = ( a2 - x2 )1/2.
A circle has an eccentricity of 0.
PI is the ratio of diameter and circumference of a circle. It is a Transcendental Number.
Plane Curve. A Plane Curve is defined by its eccentricity:
= 0 = Circle
> 0 and < 1 = Ellipse
= 1 = Parabola
> 1 = Hyperbola
Eccentricity is the relationship between the height and width of an ellipse ie if a is the width, and b is the height the eccentricity = ( 1 - a2 / b2 )½
If a = b, which is the case for a Circle, the eccentricity is 0.
If a / b, or b / a is less than 1 then it is an Ellipse.
Culture, General Things, Mathematics, Geometry, Eccentricity
Ellipse. An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
The equation for a standard ellipse with width 2a and height 2b is ( x2 / a2 ) + ( y2 / b2 ) = 1.
An ellipse has an eccentricity of > 0 and < 1.
Circle. A circle is an ellipse with equal width and height; a = b.
The ellipse equation when a = b: x2/a2 + y2/a2 = 1 or simplified ( x2 + y2 ) / a2 = 1 or y = ( a2 - x2 )1/2.
A circle has an eccentricity of 0.
Culture, General Things, Mathematics, Geometry, Ellipse
Ellipse. An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
The equation for a standard ellipse with width 2a and height 2b is ( x2 / a2 ) + ( y2 / b2 ) = 1.
An ellipse has an eccentricity of > 0 and < 1.
Plane Curve. A Plane Curve is defined by its eccentricity:
= 0 = Circle
> 0 and < 1 = Ellipse
= 1 = Parabola
> 1 = Hyperbola
Eccentricity is the relationship between the height and width of an ellipse ie if a is the width, and b is the height the eccentricity = ( 1 - a2 / b2 )½
If a = b, which is the case for a Circle, the eccentricity is 0.
If a / b, or b / a is less than 1 then it is an Ellipse.
Culture, General Things, Mathematics, Geometry, Plane Curve
Plane Curve. A Plane Curve is defined by its eccentricity:
= 0 = Circle
> 0 and < 1 = Ellipse
= 1 = Parabola
> 1 = Hyperbola