Mathematics is the study of topics such as quantity, structure, space, and change. It is used in many fields including science, engineering, and finance. Art includes activities that create visual works, performing arts, literature, and other media. Mathematics and art are closely related through concepts like fractals, the golden ratio, symmetry, patterns, and geometric shapes that appear in both natural and human-made works. Many artists use mathematical principles in their compositions to achieve balance, proportion and other aesthetic goals.

3. MATHEMATICS
Mathematics is the study of topics such
as quantity (numbers), structure,
space, and change. There is a range of views
among mathematicians and philosophers as
to the exact scope and definition of
mathematics. Mathematics is used throughout
the world as an essential tool in many fields,
including natural science, engineering,
medicine, finance and the social sciences.

4. DO YOU REMEMBER………????

6. ART….
Art is a diverse range of human activities ;
which includes the creation of images or
objects in fields including painting,
sculpture, printmaking, photography, and
other visual media. Architecture is often
included as one of the visual arts; for
example. Music, theatre, film, dance, and
other performing arts, as well as literature and
other media such a sinter active media, are
included in a broader definition of art

8. MATHEMATICS AND ART

9. Maths is all about
patterns and rhythms, so
it's no surprise that
there's plenty of maths in
art. Whether it's the
visual arts or the
performing arts, maths
can be a tool, an
inspiration, or simply
something that's
naturally contained
within the structures and
patterns.

10. • Fractals
• Golden ratio
• Symmetry
• Patterns and series
• Golden rectangle
• In fashion designing
• Illusion
• Geometric abstractionism
• Tessellations
• Origami
• Anamorphic Art

11. A fractal is a natural phenomenon or a mathematical set that exhibits a
repeating pattern that displays at every scale. If the replication is exactly
the same at every scale, it is called a self-similar pattern. Fractals can
also be nearly the same at different levels.
Applications:
Such patterns are also found in;
• Cauliflower and Broccoli is a natural fractal structure.
• And the butterfly effect is also said to be natural fractal
• It is also found in African art and architecture.
• Found in Mountain ranges and river networks.
• Found in Snow flakes , ocean waves , earth quakes etc…
• Human lungs ( bronchi) also has fractal parts in it

13. The Golden Ratio, roughly equal to 1.618,
was first formally introduced in text by
Greek mathematician Pythagoras and later
by Euclid in the 5th century BC. Many works
of ancient art exhibit and incorporate the
golden ratio in their design. It can be seen in
Egyptian, Greek vases, Chinese pottery,
Olmec sculptures from as early as the late
Bronze Age.

16. Symmetry in everyday language refers to a sense of
harmonious and beautiful proportion and balance.
Application :
• In fruits,flowers and in other parts of the plants.
• in feathers of birds
• in art and architecture
• in snowfalkes and in other natural phenomenon’s
• in sea animals such as dolphins and star fishes

18. GEOMETRIC PATTERNS:
Simple arrangements of mathematical figures, like circles and
triangles, have been extensively used in decoration throughout
history. For example, the "Flower of Life" can be seen on the
Temple of Osiris at Abydos, Egypt, which dates back about 5,000
years .
APPLICATION:

19. By definition, the first two numbers in the Fibonacci sequence are 1
and 1, or 0 and 1, depending on the chosen starting point of the
sequence, and each subsequent number is the sum of the previous
two. The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Applications:
In flowers such as daisy , sunflower etc.
In fruits such as pine apple
In shells of the sea animals
In galaxies i. e in our milky way galaxies…

21. The Golden Rectangle is considered to be one of the
most pleasing and beautiful shapes to look at, which is
why many artists have used it in their work . The two
artists, who are perhaps the most famous for their use
of the golden rectangle, are Leonardo Da Vinci and Piet
Mondrian.
Mona Lisa, is one of the most famous paintings in the
world, and is a very good example of Da Vinci's use of
the golden rectangle in art. If you draw a rectangle
around Mona Lisa's face, that rectangle will turn out to
be golden. The dimensions of the painting itself also
form a golden rectangle.

23. All aspects require arithmetic and math. Most notably,
math is used in Pattern design and drafting. Patterns
are drafted using measurement charts and complex
math. It's not easy to turn something flat, such as paper
or fabric, and make it into a three dimensional shape,
the human body! Drafting is a series of measurements
and calculations .

25. • An illusion is a distortion of the art, revealing how the brain
normally organizes and interprets sensory stimulation.
• The Seven Basic Kinds of Illusions ;
1. Height-Width Illusion
2. Illusion of Interrupted Extent
3. Illusion of Contour
4. Equivocal Illusion
5. Illusion of Depth
6. Illusion of Contrast
7. Non-Classified Illusions

26. GEOMETRIC ABSTRACTIONISM
Piet Mondrian was one of the founding members in 1917 of a
Dutch art movement. Mondrian's style of painting involved the use
of strictly horizontal or vertical black lines to create a grid of
rectangles, some of which were filled in with black or white, or
vivid red, blue or yellow.
So he tried to create paintings by only these fundamentals and
their relationship with each other, using only the prime colours and
elements of geometric mathematics - straight lines, right angles
and quadrangles - to create his reflection of reality.

27. Maurits Cornelis Escher is well known for his graphic art. He
enjoyed playing with aspects of surfaces and reflection,
perspective, symmetry, and impossible figures such as the
paradoxical staircase depicted in Ascending and Descending. He
also produced a great number of tessellating patterns composed
of irregular shapes. Escher made an art form out of colorful
patterns of tessellating reptiles, birds, fish and even crabs and
sea-horses.

29. Origami is the Japanese craft of creating wonderful
three-dimensional shapes and models solely by folding
paper - usually a single square sheet
• ORI – PAPER
• KAMI - FOLDED
The links between this ancient art and mathematics are
profound. If you unfold a finished model you will see a
complex geometrical pattern of creases made up of
triangles and squares, many of which will be congruent
.

30. ANAMORPHIC ART
"Anamorphic" is a form of art that was first experimented with
during the Renaissance and became particularly popular during
the Victorian era. It involves distorting an image so that it is
unrecognizable unless viewed in the right way.
Anamorphic art is a good demonstration of the mathematics of
transformations. Translations, rotations and reflections don't tend
to distort an object in interesting ways, but stretching along one
axis is a popular method.

31. CONCLUSION
The world around us is full of relationships, rhythms,
correlations, patterns. And mathematics underlies all of
these, and can be used to predict future outcomes. Our
brains have evolved to survive in this world: to analyze
the information it receives through our senses and spot
patterns in the complexity around us. In fact, it's
thought that the mathematical structure embedded in
the rhythm and melody of music is what our brains latch
on to, and that this is why we enjoy listening to it. It is
perhaps not surprising then that there is a great deal of
overlap between mathematics and the art that our brain
finds so pleasing to look at.

33. IDHAYAPRIYA.I
INDHIRA.B
ALLWYN BERNET SAMUEL.D