Mathematics related Quotes in Images

Here comes some of the quotes which I considered dear to my heart.

These images are taken from Google Images.

                         

 

FIELD'S MEDAL

Hai friends. Today we are going to discuss about field's medal which is nothing but the highest award given in the field of mathematics. Everyone know that mathematicians doesn't have place in nobel prize. This is considered as Nobel prize of mathematicians and in contrast to it awarded it is awarded once in four years. It has another major restriction that the person need to be less than 40 years of age in 1st January  of that year.The monetary award is much lower than the 8,000,000 Swedish kronor (roughly 1,400,000 Canadian dollars).

It was started on the year of 1936 from then till now nearly 54 persons have been honored with this award. The last one was awarded in the year 2014.

Here comes the list of persons who got the medals with the places where they got and year.

2014	Seoul, South Korea	Artur Avila
		Manjul Bhargava
		Martin Hairer
		Maryam Mirzakhani
2010	Hyderabad, India	Elon Lindenstrauss
		Ngô Bảo Châu
		Stanislav Smirnov
		Cédric Villani
2006	Madrid, Spain	Andrei Okounkov
		Grigori Perelman(declined)
		Terence Tao
		Wendelin Werner
2002	Beijing, China	Laurent Lafforgue
		Vladimir Voevodsky
1998	Berlin, Germany	Richard Borcherds
		Timothy Gowers
		Maxim Kontsevich
		Curtis T. McMullen
1994	Zurich, Switzerland	Jean Bourgain
		Pierre-Louis Lions
		Jean-Christophe Yoccoz
		Efim Zelmanov
1990	Kyoto, Japan	Vladimir Drinfeld
		Vaughan F. R. Jones
		Shigefumi Mori
		Edward Witten
1986	Berkeley, US	Simon Donaldson
		Gerd Faltings
		Michael Freedman
1982	Warsaw, Poland	Alain Connes
		William Thurston
		Shing-Tung Yau
1978	Helsinki, Finland	Pierre Deligne
		Charles Fefferman
		Daniel Quillen
		Grigori Margulis
1974	Vancouver, Canada	Enrico Bombieri
		David Mumford
1970	Nice, France	Alan Baker
		Heisuke Hironaka
		John G. Thompson
		Sergei Novikov
1966	Moscow, USSR	Michael Atiyah
		Paul Joseph Cohen
		Alexander Grothendieck
		Stephen Smale
1962	Stockholm, Sweden	Lars Hörmander
		John Milnor
1958	Edinburgh, UK	Klaus Roth
		René Thom
1954	Amsterdam, Netherlands	Kunihiko Kodaira
		Jean-Pierre Serre
1950	Cambridge, US	Laurent Schwartz
		Atle Selberg
1936	Oslo, Norway	Lars Ahlfors
		Jesse Douglas

REFERENCE: Wikipedia

SOLID GEOMETRY CONTINUES...

To be frank, I don't know how to define pyramid.

Parts of the Pyramid:

• Base
• Apex

Pyramid:

A pyramid is formed by connecting a base to an apex.

Actually Whenever we start with pyramid. All of us a sudden what we get in our mind is the Great pyramid of Egypt. But it is a type of pyramid.

We have different types of pyramid based on their bases. They are

• Triangular Pyramid
• Square Pyramid
• Pentagonal Pyramid

In detail when taken in account, the following gives

Triangular Pyramid:

It has four faces in which three sides are triangles and the base is also a triangle  where four vertices with six edges are present also known as tetrahedron.

Square Pyramid:

It has five faces in which four side faces are triangles and base is a square where five vertices and eight edge are present.

Pentagonal Pyramid:

This has six faces in which five side faces are triangles and base is a pentagon where six vertices and ten edges are present.

Again they are divided into two types based on apex position. They are 

• Right pyramid where the apex is straightly above the base.
• Oblique Pyramid  where it is not straight.

And then again into two types based on their Bases. They are

• Regular Pyramid when the base is a regular polygon.
• Irregular Pyramid when the base is a irregular polygon.

This is  what I know about Pyramid. These images are taken from Google images.

SOLID GEOMETRY CONTINUES....

Next what we are going to see is Prism.

PRISM:

A prism is a solid object with identical ends, flat faces and the same cross section all along its length. Here cross section is nothing but a straight line cut across the object.

This cross section which is formed looks like a triangle. So it is known as triangular prism.

As it comes under the polyhedron, it has only flat surfaces and no curves. The parts of the prism were

• Bases ( the ends of the prism were parallel and they are bases )
• Sides ( the side faces of a prism were parallelograms and it has the property of a parallelogram)

There are six types of prism. They are

• Square prism i.e cube.
• cuboid i.e rectangular prism.
• Triangular prism.
• Pentagonal prism.
• Hexagonal prism
• Oblique Prism.

.

Again the prism are divided into two types based on their cross section. They are

• Regular prism
• Irregular prism

Whatever we have discussed above is all the examples of regular prism because they have regular cross-section and the cross-section are irregular in irregular prisms.

These images are taken from google images

The next topic is nothing but Pyramids. We will see in later classes.

SOLID GEOMETRY CONTINUES....

When moving into the types, we had two types.  Now we will move onto the first one i.e Polyhedron.

Polyhedron as said before it must have flat surfaces. When moving into their types, we will start with cubes and cuboids.

Cube:

A cube is a polyhedron with six faces and all its faces are equal in length and breadth.

Properties:

• It has 6 faces.
• Each face will be having 4 edges looking like a square.
• In total, it has 12 edges.
• It has 8 vertices's i.e corners.
• In each vertex 3 edges meet each other.
• It also comes under the platonic solids.

As it  has six faces, it is known as hexahedron.

Example: simple dice we used to play ladder games.

 we will see formula's and about them in detail later.

CUBOID:

A cuboid is a box-shaped object which has different length, width and depth.

PROPERTIES:

• It has six flat surfaces 
• All angles are right angles.
• All its face are in rectangles.
• It also looks like prism because it has some cross-section along a length. 
• Also a rectangular prism.
• It becomes a square prism when two of its length become equal.

Example: Cardboard box, Pencil Box, bricks,...

Platonic Solid:

A platonic solid is also a 3-D shape in which each face is the same regular polygon and the same number of polygons meet at each vertex.

There are only five types of platonic solids. They are

• Tetrahedron
• cube
• octahedron
• dodecahedron
• icosahedron

SOLID GEOMETRY

Solid geometry is the geometry of three dimensional figure. They are 3-D figures.The kind of space where we live in today.

They are called three dimensional because they have height, width and depth. While plane geometry has only height and width.

They can be divided into two types. They are

• Polyhedra (They must have flat surfaces)
• Non-Polyhedra ( They don't have any flat surfaces)

Polyhedra has four different types. They are

• Cubes and cuboids
• Platonic solids
• Prisms 
• Pyramids

Non-Polyhedra also has four different types. They are

• Sphere
• Torus 
• Cone
• Cylinder.

Solid have three properties. They are

• Volume 
• Surface Area
• they have vertices, faces and edges.

Today we will start with vertices, faces and edges. 

Vertex and Vertices:

A vertex is a corner nothing but you people denote the points like A,B,C,D,..... The plural form is Vertices having more than one.

FACE AND FACES:

A face is an  individual surface like the one side of plane. Similarly plural form is faces.

EDGE AND EDGES:

An edge is an line segment joining two vertices nothing but the line between and b, c and d like that it goes on. As said above the plural form is Edges.

We will see them in later when we go deeply.

CIRCLE

Circle is also a two dimensional plane figure. The only difference is that it has no sides.

Circle is nothing but the set of all points that are in same distance from the centre.

Circle has three things in it. Now they are

• Radius i.e distance from the center onward.
• Diameter i.e it is a line drawn across the center in a circle.
• Circumference i.e Distance once around the circle.

And in detail to define we have 

• Diameter= 2*radius
• Circumference=2*π*radius.

image of a circle

COMPOUND INTEREST

INTRODUCTION

•  How many of you have been to bank with your parents?
•  What have you observed in bank?
• What is the main purpose of bank?
• Why we need to deposit money in bank?   
• We could also keep it in our home.Why the need?
• What is the reason behind depositing money in bank ?

Simple interest:

When interest is paid only on the principle alone is known as simple interest.

formulas for simple interest

COMPOUND INTEREST:

The interest which is paid on the principle as well as on the accured interest is called as compound interest.

Explanation:

• Consider vinay has borrowed Rs.50,000 from bank with 4% rate of interest for two years.
• Vinay has to pay Rs.2000 as interest in the first year.
• If he couldn’t pay it then the interest  will be added to the principle i.e. Sum = principle + interest
• Sum = Rs.50000+ Rs.2000 = Rs.52000.
• Now vinay has to pay interest in the second year with Rs.52000 as new principle.
•  This way of calculating interest is known as compound interest.

Types of compound interest:

When compounded quarterly:

When compounded half-yearly:

When compounded annually:

Problem for example:

DIFFERENCE BETWEEN SI AND CI:

Real life applications:

These are some features which gives profit

•      Provident fund

•      Bank deposits

Negative features

•      Credit card bills

•      Loans

CONCLUSION: