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In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.
Therefore, it is not opposite day, but if you say it is a normal day it would be considered a normal day, which contradicts the fact that it has previously been stated that it is an opposite day. Richard's paradox : We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
In elliptic geometry we see a typical example of this. [1]: 108 In the spherical representation of elliptic geometry, lines are represented by great circles of a sphere with diametrically opposite points identified. In a different model of elliptic geometry, lines are represented by Euclidean planes passing through the origin. Even though these ...
Lines and are antiparallel with respect to the line if they make the same angle with in the opposite senses. Two lines l 1 {\displaystyle l_{1}} and l 2 {\displaystyle l_{2}} are antiparallel with respect to the sides of an angle ∠ A P C {\displaystyle \angle APC} if they make the same angle in the opposite senses with the bisector of that angle.
For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
The two line segments connecting opposite points of tangency have equal length. The tangent lengths, distances from a point of tangency to an adjacent vertex of the quadrilateral, are equal at two opposite vertices of the quadrilateral. (At each vertex, there are two adjacent points of tangency, but they are the same distance as each other from ...
A typical example is the proof of the proposition "there is no smallest positive rational number": assume there is a smallest positive rational number q and derive a contradiction by observing that q / 2 is even smaller than q and still positive.
As λ or μ varies, the hyperboloid is generated. The two sets represent a regulus and its opposite. Using analytic geometry, Bell proves that no two generators in a set intersect, and that any two generators in opposite reguli do intersect and form the plane tangent to the hyperboloid at that point. (page 155).
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