2. Mathematics as an art of calculation;
◦ Mathematics and art are related in a variety of ways. Mathematics has itself
been described as an art motivated by beauty. Mathematics can be discerned in
arts such as music, dance, painting, architecture, sculpture, and textiles.
◦ Artists have used mathematics since the 4th century BC when the
Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on
the ratio 1:√2 for the ideal male nude.
◦ The engraver Albrecht Dürer made many references to mathematics in his
work Melencolia I. In modern times, the graphic artist M. C. Escher made
intensive use of tessellation and hyperbolic geometry, with the help of the
mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van
Doesburg and Piet Mondrian explicitly embraced geometrical forms.
◦ Mathematics has inspired textile arts such as quilting, knitting, cross-
stitch, crochet, embroidery, weaving, Turkishand other carpet-making, as well
as kilim.
3. ◦ Mathematics has directly influenced art with conceptual tools such as linear
perspective, the analysis of symmetry, and mathematical objects .
◦ . Mathematical references include a compass for geometry, a magic square and
a truncated rhombohedron, while measurement is indicated by the scales
and hourglass.[1]
◦ In classical times, rather than making distant figures smaller with linear
perspective, painters sized objects and figures according to their thematic
importance. In the Middle Ages, some artists used reverse perspective for
special emphasis.
◦ The rudiments of perspective arrived with Giotto (1266/7 – 1337), who attempted
to draw in perspective using an algebraic method to determine the placement of
distant lines. In 1415, the Italian architect Filippo Brunelleschi and his
friend Leon Battista Alberti demonstrated the geometrical method of applying
perspective in Florence, using similar triangles as formulated by Euclid, to find
the apparent height of distant objects.
5. Mathematics as a language
◦ The notion that Mathematics is a language is held by many mathematicians and is being
expressed on frequent occasions
◦ The language of mathematics is the system used by mathematicians to communicate
mathematical ideas among themselves.[1] This language consists of a substrate of some natural
language (for example English) using technical terms and grammatical conventions that are
peculiar to mathematical discourse (see Mathematical jargon), supplemented by a highly
specialized symbolic notation for mathematical formulas.
◦ Mathematical notation is central to the power of modern mathematics.
◦ The mathematical notation used for formulas has its own grammar, not dependent on a specific
natural language, but shared internationally by mathematicians regardless of their mother
tongues.[5] This includes the conventions that the formulas are written predominantly left to right,
even when the writing system of the substrate language is right-to-left, and that the Latin
alphabet is commonly used for simple variables and parameters
6. ◦ A formula such as
◦ sin x + a cos 2 x ≥ 0
is understood by Chinese and Syrian mathematicians alike.
◦ Such mathematical formulas can be a part of speech in a natural-language phrase, or even
assume the role of a full-fledged sentence. For example, the formula above, an inequation, can
be considered a sentence or an independent clause in which the greater than or equal to
symbol has the role of a symbolic verb. In careful speech, this can be made clear by
pronouncing "≥" as "is greater than or equal to", but in an informal context mathematicians may
shorten this to "greater or equal" and yet handle this grammatically like a verb. A good example
is the book title Why does E = mc2?;
7. Mathematics as a way of thinking
◦ In the twenty-first century, everyone can benefit from being able to think mathematically. This is
not the same as “doing math.”
◦ The latter usually involves the application of formulas, procedures, and symbolic manipulations;
◦ mathematical thinking is a powerful way of thinking about things in the world -- logically,
analytically, quantitatively, and with precision. It is not a natural way of thinking, but it can be
learned. Mathematicians, scientists, and engineers need to “do math,” and it takes many years
of college-level education to learn all that is required.
