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 - a^{2} / b^{2} )^{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: x^{2}/a^{2} + y^{2}/a^{2} = 1 or simplified ( x^{2} + y^{2} ) / a^{2} = 1 or y = ( a^{2} - x^{2} )^{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 ( x^{2} / a^{2} ) + ( y^{2} / b^{2} ) = 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 - a^{2} / b^{2} )^{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 ( x^{2} / a^{2} ) + ( y^{2} / b^{2} ) = 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 environs^{1}. 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