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One very unique aspect of
Variable Shape Geometry is that a two-sided shape can be formed using the Parabolism Postulate. Later, complex two-gons can be formed because of a "Differential Angles Postulate" causing new types of parallel/parallo lines, but in the basic form, two-gons can only be "Bess
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As does
Euclidean and Non-Euclidean Geometry, Variable Shape Geometry starts off with the basic line/point theorems and postulates (such as the Distance Postulate) to lay a foundation for the Parabolism Postulate. Before it can be postulated however, "parallel" lines must be introduced. Here, lines
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Variable Shape
Geometry strays away from the traditional Angle Sum Theorem (angles of a triangle add up to 180 degrees) and uses the Parabolism Postulate. With it, triangles with two right angles can be formed where the third angle is the measure of the arc formed by the parallo lines (due to the
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end after the "Congruency
Postulate" is introduced. It allows two-gons to be proven to be triangles, triangles to be proven to be squares, squares to be proven to be pentagons, and so on until two-gons/triangles/square/etc.. are proven to be infinite-sided shapes in which case everything is a
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is usually the "Differential Angles
Postulate" which spawns different parallo lines; ones that intersect before use of the Parabolism Postulate. Later, the "Indiminency Postulate" is introduced which forms "indiminent" lines; curved parallo lines.
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When viewing
Variable Shape Geometry as a whole, due to the fact that "everything is everything", nothing can be done. But if one were to prove that everything was in fact everything at the very end, then there is room to study individual shapes.
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If two lines are considered to be parallo, then two corresponding points on the line can be connected in an arc to form a parabola. When dealing with closed polygons, the parabola is not considered a side on its own.
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Advanced
Variable Shape Geometry comes after the set of theorems that is associated with the individual shapes and their properties. The first postulate that marks the beginning of what is called
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Like the triangles, unlikely squares can be formed using the
Parabolism Postulate. The "Bess square" is a square with three obtuse angles (which is impossible with a traditional square).
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One of the main concepts of
Variable Shape Geometry is that it modifies Euclid's Parallel Postulate as does Non-Euclidean Geometry but not in the same way. Instead it establishes the
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as does
Euclidean Geometry to be considered parallel. However, parallel does not mean the lines never intersect in Variable Shape Geometry, so the term introduced for these lines is
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right angles). Triangles with two right angles are traditionally called "Bess triangles". Later on, triangles can be proven to be squares because of the
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In this context, "corresponding points" refers to points that are on a perpendicular line to the parallo lines. In basic
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that are cut by a transversal must have congruent alternate interior, corresponding, or alternate exterior
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A common Bess square formed using three obtuse angles and the Parabolism Postulate.
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A common Bess triangle formed using two right angles and the Parabolism Postulate.
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A Bess two-gon formed using two parallo lines and the Parabolism Postulate.
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Unlike other types of geometry, Variable Shape Geometry has a
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129:construction (such as in the image), the
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212:Advanced Variable Shape Geometry
95:The Parabolism Postulate in use.
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74:"Everything is everything"
119:The Parabolism Postulate
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241:References
158:Triangles
106:"parallo"
70:pentagons
58:triangles
52:The name
261:Geometry
255:See also
127:parabola
116:—
39:Val Bess
35:geometry
195:Two-gon
179:Squares
145:ovals.
66:squares
62:squares
231:circle
149:Shapes
143:oblong
139:oblate
102:angles
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131:arc
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