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Historically, alterable objects of art have existed since the Renaissance, for example, in the Triptych "The Garden of Earthly Delights" by Hieronymus Bosch or in the so-called "alterable altarpieces", such as the Isenheim Altarpiece by Matthias Grünewald, or Albrecht Dürer's Paumgartner altarpiece, where changing motifs could be revised in accord with the changing themes of the ...
When reduced modulo a prime p, there is an analogous theory to the classical theory of complex modular forms and the p-adic theory of modular forms. Reduction of modular forms modulo 2 [ edit ]
Examples of modular origami made up of different variations of Sonobe units.. Modular origami can be classified as a sub-set of multi-piece origami, since the rule of restriction to one sheet of paper is abandoned.
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S.
It is easy to show that the trace of a matrix representing an element of Γ(N) cannot be −1, 0, or 1, so these subgroups are torsion-free groups. (There are other torsion-free subgroups.) The principal congruence subgroup of level 2, Γ(2), is also called the modular group Λ. Since PSL(2, Z/2Z) is isomorphic to S 3, Λ is a subgroup of index 6.