M A T H E M A

T I C S

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.

DO YOU REMEMBER………????

ART

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

?

MATHEMATICS AND ART

MATH IN ARTMaths 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.

Let’s further look into…..• Fractals

• Golden ratio

• Symmetry

• Patterns and series

• Golden rectangle

• In fashion designing

• Illusion

• Geometric abstractionism

• Tessellations

• Origami

• Anamorphic Art

FRACTALSA 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

GOLDEN RATIO

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.

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

PATTERNS AND SERIESGEOMETRIC 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:

FIBONACCI SERIES

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…

 

GOLDEN RECTANGLE

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. 

FASHION DESIGNINGAll 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 .

ILLUSION• 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

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.

TessellationsMaurits 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.

Origami …..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 .

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. 

CONCLUSIONThe 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.

IDHAYAPRIYA.I

INDHIRA.B

ALLWYN BERNET SAMUEL.D

THANK YOU..