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15 Cards in this Set
- Front
- Back
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Area
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a function from the set of straight edged figures to the real numbers with certain properties, namely, that two equivalent figures will have the same area value
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equivalent figures
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two figures are equivalent if they can each be partition into equal sets of congruent triangles
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triang with maximum area
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a triangle with three ideal vertices
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defect of a quadrilateral
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2pi minus the sum of the 4 angles
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corresponding points
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given two lines l and m and a point A on l, we say that B corresponds to A or that A and B are correspponding points if the angle formed at A on one side of line AB with line l is the same as the angle formed at B on the same side of line AB with line m
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limiting curve
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given the set of all lines that are limiting parallels to a line l and a point A on l, the limiting cirve through A is the set of all points on the lines in the set which correspond to A, including A (we think of the set of limiting paralells as all of the lines which go through the same ideal point
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equidistant curve
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given the set of all lines that share a common perpondicular, m, with a line l and a point A on l, the equidistant curve through A is the set of all points on the lines in the set which correspond to A including A (we think of it as the set of divergent parallels which throuh the ultra-ideal point
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concentric limiting curves
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two limiting curves which are distinct but who points are the same set of limiting parallels. (The one in the direction of parallelism is considered to be the one "inside" the other).
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radius
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one of the lines in the sets of lines used to find a limiting curve or an equidistant curve.
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notation for right triangle
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lambda = measure of angle A
mu = measure of angle B l = length whose angle of parallelism is lambda m = length whose angle of parallelism is mu lambda' = complement of lambda mu' = complement of mu l' = length whose angle of parallelism is lambda' m' = length whose angle of parallelism is mu' alpha = the angle of parallelism for length a beta = the angle of parallelism for length b gamma = the angle of parallelism for length c alpha' = complement of alpha beta' = complement of beta gamma' = complement of gamma a' = length whose angle of parallelism is alpha' b' = length whose angle of parallelism is beta' c' = length whose angle of parallelism is gamma' |
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arc length
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if s is an arc length, it is the number of arcs of length 1 that it takes to produce it. By using limits, this number may be a real number.
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unit arc length
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Let AB be an arc of a limiting curve with radii AOmega and BOmega. If the angle generated at A by line AB and AOmega is pi/4, then the arc length of AB is 2S and S is the unit arc length.
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coordinate of a point P
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Given two perpendicular lines X and Y with intersection point O, the coordinate of point P is the pair P(x,y) where y in the length of the segment PPx where Px is the foot of the perpendicular to X through point P, and x is the length of the segment OPx. (Note, in hyperbolic geometry, if we let Py be the foot of the perpendicular to Y through P, and y' be the length of segment PPy, then y' is not equal to y and further
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sinh x
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(exp(x) - exp(- x)) / 2
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cosh x
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(exp(x) + exp(- x)) / 2
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