INTRODUCTION
Mathematics and architecture have always been close, not only because architecture depends on developments in mathematics but also their shared search for order and beauty. We will see how mathematics is not just about formulas and logic, but about patterns, symmetry, structure, shape and beauty.
USE OF MATHEMATICS
Whether its symmetry, geometric shapes, proportion, or perspectives, math is found in all architecture. It includes
i) Symmetry (ii) Geometric shapes (iii) Proportion (iv) Perspective
SYMMETRY
The Parthenon is an architectural marvel, and it is full of symmetry. Symmetry allows the architect to bring attention to the axis of symmetry, by drawing your eyes to that point. It is at this point that the symmetrical sides a formed form.
GEOMETRIC SHAPES
Geometric shapes includei) Triangles (ii) Circles (iii) Squares (iv) Cylinders (v) Rectangles
Triangles, circles, squares are few of the geometric shapes used in everyday architecture. Geometry is found in almost all buildings. Even those that are in the exceptions have some structure based formed from a geometric shape. Geometry is a part of day to day architecture. It plays an important role in architecture.
USE OF SHAPES
Circle
Square
Triangle
PROPORTION
The golden number of proportion is found in lot of architecture. In short, this means that the ratios of different dimensions are extremely similar throughout the building. To be exact the ratio must be some where near to 1.6 . not all proportions are just by number though. Architects also use proportion in order to emphasize the importance of different areas of a building and its surrounding. Lets see few images to get a better understanding:-
USE OF PROPORTION
2 3 1
GOLDEN RATIO
Given two quantities, when the ratio of the larger quantity to the smaller one is equal to the ratio of the sum of the quantities to the larger one, then it is said to be a golden ratio.
The golden ratio (symbol is the Greek letter PHI ) is a special number approximately equal 1.618.
It appears many times in geometry, art, architecture and other areas.
HOW TO CALCULATE GOLDEN RATIO?
IF you divide lines into two parts such that :the longer part divided by the smaller part is also equal to the whole length divided by the longer part then you will have the golden ratio
EXAMPLES
(1) Let a=7 and b=3, so a+b= 10: 7/3= 2.333 but 10/7=1.429 (2) Let a=6 and b=4 so a+b= 10: 6/4= 1.5, but 10/6= 1.666 so that wont work
closer but not there yet!
(3) Let a=6.18 and b=3.82 so a+b=10: 6.18/3.82= 1.6178 , and 10/6.18= 1.618 we have found the golden ratio
that s it.
USE OF |PHI}
Pyramids
Parthenon
Tajmahal
PERSPECTIVE
This allows you to see buildings in many different ways than just one.
This is a tool used by many architects in order to make things appear differently than they truly are.
Much perspective is done with the geometric shape of a rectangle and square.
USE OF PERSPECTIVE
Left hand side view
Right hand side view
Front view
CONCLUSION
Mathematics is a very integral part of architecture. It is found in nearly all architecture no matter how you look at it. One can argue also that different types of math are found in the same piece of architecture. Math is a tool that an architect must use in order to make a good building. Hence Architecture includes Mathematics in it
Submitted to:- Prof. Mayura
doc_724572225.pptx
Mathematics and architecture have always been close, not only because architecture depends on developments in mathematics but also their shared search for order and beauty. We will see how mathematics is not just about formulas and logic, but about patterns, symmetry, structure, shape and beauty.
USE OF MATHEMATICS
Whether its symmetry, geometric shapes, proportion, or perspectives, math is found in all architecture. It includes
i) Symmetry (ii) Geometric shapes (iii) Proportion (iv) PerspectiveSYMMETRY
The Parthenon is an architectural marvel, and it is full of symmetry. Symmetry allows the architect to bring attention to the axis of symmetry, by drawing your eyes to that point. It is at this point that the symmetrical sides a formed form.
GEOMETRIC SHAPES
Geometric shapes include
i) Triangles (ii) Circles (iii) Squares (iv) Cylinders (v) RectanglesTriangles, circles, squares are few of the geometric shapes used in everyday architecture. Geometry is found in almost all buildings. Even those that are in the exceptions have some structure based formed from a geometric shape. Geometry is a part of day to day architecture. It plays an important role in architecture.
USE OF SHAPES
Circle
Square
Triangle
PROPORTION
The golden number of proportion is found in lot of architecture. In short, this means that the ratios of different dimensions are extremely similar throughout the building. To be exact the ratio must be some where near to 1.6 . not all proportions are just by number though. Architects also use proportion in order to emphasize the importance of different areas of a building and its surrounding. Lets see few images to get a better understanding:-
USE OF PROPORTION
2 3 1
GOLDEN RATIO
Given two quantities, when the ratio of the larger quantity to the smaller one is equal to the ratio of the sum of the quantities to the larger one, then it is said to be a golden ratio.
The golden ratio (symbol is the Greek letter PHI ) is a special number approximately equal 1.618.
It appears many times in geometry, art, architecture and other areas.
HOW TO CALCULATE GOLDEN RATIO?
IF you divide lines into two parts such that :the longer part divided by the smaller part is also equal to the whole length divided by the longer part then you will have the golden ratio
EXAMPLES
(1) Let a=7 and b=3, so a+b= 10: 7/3= 2.333 but 10/7=1.429 (2) Let a=6 and b=4 so a+b= 10: 6/4= 1.5, but 10/6= 1.666 so that wont work
closer but not there yet!
(3) Let a=6.18 and b=3.82 so a+b=10: 6.18/3.82= 1.6178 , and 10/6.18= 1.618 we have found the golden ratio
that s it.
USE OF |PHI}
Pyramids
Parthenon
Tajmahal
PERSPECTIVE
This allows you to see buildings in many different ways than just one.
This is a tool used by many architects in order to make things appear differently than they truly are.
Much perspective is done with the geometric shape of a rectangle and square.
USE OF PERSPECTIVE
Left hand side view
Right hand side view
Front view
CONCLUSION
Mathematics is a very integral part of architecture. It is found in nearly all architecture no matter how you look at it. One can argue also that different types of math are found in the same piece of architecture. Math is a tool that an architect must use in order to make a good building. Hence Architecture includes Mathematics in it
Submitted to:- Prof. Mayura
doc_724572225.pptx