By J. Dennis Lawrence

ISBN-10: 0486602885

ISBN-13: 9780486602882

Forty years after its preliminary ebook, this quantity keeps to rank one of the field's most-cited references. one of many greatest and most interesting on hand collections, the catalog covers basic homes of curves and kinds of derived curves. The curves and the values in their parameters are illustrated through approximately ninety pictures from a CalComp electronic incremental plotter.
Suitable for college students and researchers in geometry and computing device technology, the textual content starts off by way of introducing basic houses of curves and kinds of derived curves. next chapters follow those homes to conics and polynomials, cubic and quartic curves, algebraic curves of excessive measure, and transcendental curves. a complete of greater than 60 unique curves are featured, each one illustrated with a number of CalComp plots containing curves in as much as 8 varied versions. Indexes offer tables of derived curves, curve names, and a 95-item consultant to additional reading.

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Extra resources for A Catalog of Special Plane Curves

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C x/ D cos b: (B) Comparing the values of sin p given in (A) and (B) gives sin a sin B D sin b sin A: (6) Dividing both sides of the last equation in Group (B) by both sides of the last equation in Group (A) gives cos b tan x D cot c: cos a sin c The combination of the second, third and last equations in (A) gives tan x D tan a cos B: Comparing these two values of tan x leads us to the equation cos b cos a cos c D sin a sin c cos B: 20 (7) Pangeometry 21 Likewise, if the perpendicular p falls outside the triangle and adds the arc x to the arc c, and the angle D to the angle C , there arise two right spherical triangles.

Parallel to a. b/. ˛/; which is the equation that we found above, and which is therefore proven in all cases. x/ D for x D 1, which agrees with what we have adopted and proved above. ˇ/ and 2 . c/: 44 There is an equivalent formula in Lobachevsky’s first published memoir, the Elements of geometry x x (1829) ([95], p. x/ D e 2e . a/: (12) Now let a, b, c be the three edges of an arbitrary rectilinear triangle and let A, B, C be the angles opposite to these edges. Let us drop from the vertex of the angle C a perpendicular p on the edge c.

Parallel to a. b/. ˛/; which is the equation that we found above, and which is therefore proven in all cases. x/ D for x D 1, which agrees with what we have adopted and proved above. ˇ/ and 2 . c/: 44 There is an equivalent formula in Lobachevsky’s first published memoir, the Elements of geometry x x (1829) ([95], p. x/ D e 2e . a/: (12) Now let a, b, c be the three edges of an arbitrary rectilinear triangle and let A, B, C be the angles opposite to these edges. Let us drop from the vertex of the angle C a perpendicular p on the edge c.

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A Catalog of Special Plane Curves by J. Dennis Lawrence


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