Culture, General Things, Mathematics, Geometry
Geometry is in Mathematics.
Culture, General Things, Mathematics, Geometry, Circle
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.
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.
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.
Culture, General Things, Mathematics, Geometry, Ellipse
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.
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
Culture, General Things, Mathematics, Geometry, Frustrum
Frustrum. The portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid ie a pyramind with its top cut off, or a Rolo.
Archaeologia Volume 2 Section XXXV. From this hill I made a hasty sketch of the great barrow at New Grange and its environs1. The lanes about it are planted with rows of trees. And the country forms an ornamented landscape, uncommon in Ireland. The pyramid, if I may so call it, built on a rising ground, and heaving its bulky mass, over the tops of the trees, and above the face of the country, with dimensions of a scale greater than he objects which surround it, appears, though now but a ruinous frustum: of what it once was, a superb and eminently magnificent monument.
Note 1. See Plate XIX.
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