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Draftsman's fifth method for drawing an ellipse

Ellipse Fifth Method

Draftsman's fifth method for drawing an ellipse

Draftsman's fourth method for drawing an ellipse, case 3

Ellipse Fourth Method Case 3

Draftsman's fourth method for drawing an ellipse, case 3

Diagrams showing the origins of eskers. A) A tunnel under the ice, nearly filled with sand and gravel by the subglacial stream which built up its bed to the level of the outlet. B) The same deposit after the ice melting of the supporting ice walls. Slumping has produced the characteristic steep side slopes.

Origin of Eskers

Diagrams showing the origins of eskers. A) A tunnel under the ice, nearly filled with sand and gravel…

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances from two fixed points is the square of half the distance between the points. It is a particular case of the Cassinian oval and resembles a figure 8. When the line joining the two fixed points is the axis of x and the middle point of this line is the origin, the Cartesian equation is the fourth degree equation, (((x^2)+(y^2))^2)=2(a^2)((x^2)-(y^2)). The polar equation is (ℽ^2) = 2(a^2)cos(2θ). The locus of the feet of the perpendiculars from the center of an equilateral hyperbola to its tangents is a lemniscate. The name lemniscate is sometimes given to any crunodal symmetric quartic curve having no infinite branch. The name is also sometimes given to a general class of curves derived from other curves in the way that the above is derived from the equilateral hyperbola. With these more general definitions of the lemniscate the above curve is called the lemniscate of Bernoulli.

Lemniscate

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances…

Draftsman's second method for drawing a parabola

Parabola Second Method

Draftsman's second method for drawing a parabola