Pictorial calculus for isometries

Oleg Viro

doi:10.4169/amer.math.monthly.123.1.82

Pictorial calculus for isometries

Oleg Viro

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper a new graphical calculus for operating with isometries of low dimensional spaces is proposed. It generalizes a well-known graphical representation of vectors and translations in an affine space. Instead of arrows, we use arrows framed with affine subspaces at their end points. The head to tail addition of vectors and translations is generalized to head to tail composition rules for isometries. The material of this paper is elementary and can be used even in the framework of high-school geometry.

Original language	English
Pages (from-to)	82-87
Number of pages	6
Journal	American Mathematical Monthly
Volume	123
Issue number	1
DOIs	https://doi.org/10.4169/amer.math.monthly.123.1.82
State	Published - 2016

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10.4169/amer.math.monthly.123.1.82

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title = "Pictorial calculus for isometries",

abstract = "In this paper a new graphical calculus for operating with isometries of low dimensional spaces is proposed. It generalizes a well-known graphical representation of vectors and translations in an affine space. Instead of arrows, we use arrows framed with affine subspaces at their end points. The head to tail addition of vectors and translations is generalized to head to tail composition rules for isometries. The material of this paper is elementary and can be used even in the framework of high-school geometry.",

author = "Oleg Viro",

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PY - 2016

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N2 - In this paper a new graphical calculus for operating with isometries of low dimensional spaces is proposed. It generalizes a well-known graphical representation of vectors and translations in an affine space. Instead of arrows, we use arrows framed with affine subspaces at their end points. The head to tail addition of vectors and translations is generalized to head to tail composition rules for isometries. The material of this paper is elementary and can be used even in the framework of high-school geometry.

AB - In this paper a new graphical calculus for operating with isometries of low dimensional spaces is proposed. It generalizes a well-known graphical representation of vectors and translations in an affine space. Instead of arrows, we use arrows framed with affine subspaces at their end points. The head to tail addition of vectors and translations is generalized to head to tail composition rules for isometries. The material of this paper is elementary and can be used even in the framework of high-school geometry.

UR - https://www.scopus.com/pages/publications/84975524680

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DO - 10.4169/amer.math.monthly.123.1.82

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SN - 0002-9890

VL - 123

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EP - 87

JO - American Mathematical Monthly

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Pictorial calculus for isometries

Abstract

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