Definition:Orientation of Coordinate Axes/Cartesian 3-Space/Left-Handed
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This page is about Orientation in the context of Analytic Geometry. For other uses, see Orientation.
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Definition
A Cartesian $3$-Space is defined as being left-handed if it has the following property:
Let a left hand be placed such that:
- the thumb and index finger are at right-angles to each other
- the $3$rd finger is at right-angles to the thumb and index finger, upwards from the palm
- the thumb points along the $x$-axis in the positive direction
- the index finger points along the $x$-axis in the positive direction.
Then the $3$rd finger is pointed along the $z$-axis in the positive direction.
Also see
Sources
- 1936: Richard Courant: Differential and Integral Calculus: Volume $\text { II }$ ... (previous) ... (next): Chapter $\text I$: Preliminary Remarks on Analytical Geometry and Vector Analysis: $1$. Rectangular Co-ordinates and Vectors: $1$. Coordinate Axes
- 1964: D.E. Rutherford: Classical Mechanics (3rd ed.) ... (previous) ... (next): Chapter $\text I$: Kinematics: $1$. Space and Time
- 1992: Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics ... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.2$ The Resolution of a Vector into Components
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cartesian coordinate system
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cartesian coordinate system
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): left-handed system