Plane Geometry and Complex Numbers

1962 ◽  
Vol 35 (4) ◽  
pp. 239
Author(s):  
Robert G. Blake
Keyword(s):  
Plane Geometry ◽  
Complex Numbers

Plane Geometry and Complex Numbers

1962 ◽  
Vol 35 (4) ◽  
pp. 239-242
Author(s):  
Robert G. Blake ◽  
Marlow Sholander
Keyword(s):  
Plane Geometry ◽  
Complex Numbers

scholarly journals A Curious Property of Octagons

2019 ◽  
Vol 3 (2) ◽  
pp. 01-07
Author(s):  
Rogério César dos Santos ◽  
Ana Clara Oliveira Comby ◽  
Ramires Vargas da Silva
Keyword(s):  
Plane Geometry ◽  
Complex Numbers ◽  
Analytical Geometry ◽  
Famous Theorem ◽  
Curious Property

The famous theorem of Van Aubel for quadrilaterals postulates that if squares are built externally on the sides of any quadrilateral, then the two segments that join the opposing centers of these squares are congruent and orthogonal. Inspired by this result and also by the results of Krishna, in this article we will prove the following result of plane geometry: each octagon is associated with a parallelogram, in some cases the parallelogram in question can be degenerate at a point or a segment. This is possible because of complex numbers and basics of analytical geometry.

Complex numbers and plane geometry

Resonance ◽  
2008 ◽  
Vol 13 (1) ◽  
pp. 35-53
Author(s):  
Anant R. Shastri
Keyword(s):  
Plane Geometry ◽  
Complex Numbers

Complex numbers

2006 ◽  
Author(s):  
Stephen C. Roy
Keyword(s):  
Complex Numbers

Spacetime Geometry

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Coordinate System ◽  
Special Relativity ◽  
Displacement Vector ◽  
Proper Time ◽  
Plane Geometry ◽  
Spatial Displacement ◽  
Spacetime Geometry ◽  
Space And Time ◽  
Displacement Vectors

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.

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