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Regarding Three Points in a Plane Such that Two Points Are Non-Equidistant from the Third Point and a Predicted Property of Any Curve in that Plane Connecting the Two Non-Equidistant Points

Prashanth R. Rao

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Abstract

In this paper, we give a simple proof that if there are two points A and B that are at distinct linear distances from a third point C (AC is not equal to BC), then any curve connecting the points A and B (this curve lies within the same plane containing A,B,C) must contain points such as D that lie at an intermediate distance from C, (DC is of length intermediate to AC and BC).

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What this paper is about

In this paper, we give a simple proof that if there are two points A and B that are at distinct linear distances from a third point C (AC is not equal to BC), then any curve connecting the points A and B (this curve lies within the same plane containing A,B,C) must contain points such as D that lie at an intermediate distance from C, (DC is of length intermediate to AC and BC).

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Available abstract

In this paper, we give a simple proof that if there are two points A and B that are at distinct linear distances from a third point C (AC is not equal to BC), then any curve connecting the points A and B (this curve lies within the same plane containing A,B,C) must contain points such as D that lie at an intermediate distance from C, (DC is of length intermediate to AC and BC).

Key concepts: Equidistant, Jordan curve theorem, Plane (geometry), Simple (philosophy), Point (geometry), Mathematics, Plane curve, Combinatorics

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Regarding Three Points in a Plane Such that Two Points Are Non-Equidistant from the Third Point and a Predicted Property of Any Curve in that Plane Connecting the Two Non-Equidistant Points — Research Paper | ScholarLens