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For example, if the xy-system is translated a distance h to the right and a distance k upward, then P will appear to have been translated a distance h to the left and a distance k downward in the x'y'-system . A translation of axes in more than two dimensions is defined similarly. [3] A translation of axes is a rigid transformation, but not a ...
Because translation is commutative, the translation group is abelian. There are an infinite number of possible translations, so the translation group is an infinite group . In the theory of relativity , due to the treatment of space and time as a single spacetime , translations can also refer to changes in the time coordinate .
A half-translation surface is defined similarly to a translation surface but allowing the gluing maps to have a nontrivial linear part which is a half turn. Formally, a translation surface is defined geometrically by taking a collection of polygons in the Euclidean plane and identifying faces by maps of the form z ↦ ± z + w {\displaystyle z ...
An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [ 1 ] The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems.
Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.
Shift operators are examples of linear operators, important for their simplicity and natural occurrence. The shift operator action on functions of a real variable plays an important role in harmonic analysis, for example, it appears in the definitions of almost periodic functions, positive-definite functions, derivatives, and convolution. [2]
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