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Geometry is in Mathematics.
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.
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.
The History of William Marshal was commissioned by his son shortly after William’s death in 1219 to celebrate the Marshal’s remarkable life; it is an authentic, contemporary voice. The manuscript was discovered in 1861 by French historian Paul Meyer. Meyer published the manuscript in its original Anglo-French in 1891 in two books. This book is a line by line translation of the first of Meyer’s books; lines 1-10152. Book 1 of the History begins in 1139 and ends in 1194. It describes the events of the Anarchy, the role of William’s father John, John’s marriages, William’s childhood, his role as a hostage at the siege of Newbury, his injury and imprisonment in Poitou where he met Eleanor of Aquitaine and his life as a knight errant. It continues with the accusation against him of an improper relationship with Margaret, wife of Henry the Young King, his exile, and return, the death of Henry the Young King, the rebellion of Richard, the future King Richard I, war with France, the death of King Henry II, and the capture of King Richard, and the rebellion of John, the future King John. It ends with the release of King Richard and the death of John Marshal.
Available at Amazon in eBook and Paperback format.
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.
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.
Plane Curve. A Plane Curve is defined by its eccentricity:
= 0 = Circle
> 0 and < 1 = Ellipse
= 1 = Parabola
> 1 = Hyperbola