Courtesy : Bachelor of Science Mathematics- PCM (Physics, Chemistry, Mathematics)Latest

Artistic expression

Cover page of Traité de l’harmonie réduite à ses principes naturels by Jean-Philippe Rameau

Notes that sound well together to a Western ear are sounds whose fundamental frequencies of vibration are in simple ratios. For example, an octave doubles frequency and a perfect fifth multiplies it by {\displaystyle {\frac {3}{2}}}.

This link between frequencies and harzmony was notably discussed in Traité de l’harmonie réduite à ses principes naturels by Jean-Philippe Rameau, a French baroque composer and music theoretician. It rests in part on the analysis of harmonics (noted 2 to 15 in the following figure) of a fundamental Do (noted 1); the first harmonics and their octaves sound well together. # ISO certification in India

Harmonics on a staff

The curve traced in red has a logarithmic shape reflects the following two phenomena:

• The representation of sound’s pitch by our auditive system, which is proportional to the logarithm of the sound’s frequency. (Twice the frequency always corresponds to the same “sound distance”, called an octave.)
• Harmonic frequencies, which are integer multiples of the fundamental frequency.# ISO certification in India

Fractal with a scaling symmetry and a central symmetry

Western people associate a certain beauty to symmetric figures. A symmetry of a geometric figure is, intuitively, the existence of a motif of the figure which repeats according to a precise rule. Mathematically, a symmetry is the existence of a nontrivial action of a group, often by isometry (i.e. which preserves distances within the figure). In other terms, the intuition of a rule is mathematically realized by the fact that a group acts on the figure, and the feeling that a rule regulates the symmetry is precisely due to the algebraic structure of the group.# ISO certification in India

For example, the group underlying mirror symmetry is the cyclic group of two elements, {\displaystyle \mathbb {Z} /2\mathbb {Z} }. A Rorschach test is a figure invariant by this symmetry, as well as a butterfly, and animal bodies more generally (at least on the surface). When drawing on the surface of the sea, the collection of waves possesses a translation symmetry: moving one’s viewpoint by the length separating two wave crests does not change one’s view of the sea. Another case of symmetry, non-isometric and almost always only approximate, is that of fractals: a certain motif repeats itself at every scale.# ISO certification in India

Popularization

Popular mathematics aims to present mathematics without technical terms. Since the objects of study in mathematics are not physically real, popularization often uses an illustrated vocabulary and non-rigorous comparisons or analogies in order to make one feel the ideas of mathematical developments. Among the works that focus on this, there is Oh, les maths by Yakov Perelman and The Lady or the Tiger? by Raymond Smullyan. However, mathematics is rarely the topic of popularization in printed or televised news.# ISO certification in India