In this video, let's discuss faces at Justice and what he says, and then we'll take you to Euler's
formula.
All right, now over here, let's get started with the basics.
I have a cube over here.
These are the faces.
Of the cube, that is, they are just flat surfaces.
All right, now, two faces for Cube meet at the nine segment, and we call that and it's an example
of an end.
Is this part over here?
All right.
And in the case of a cube, three adults meet at a point called the vertex, for example.
You have a vortex over here now in every shape.
It need not be three.
But in the case of a cube and for our understanding purpose in this case, you can see one, two and
three three and just meet at Vertex.
All right.
Now, the plural is vertices and the singular is vertex.
All right, now let's continue analyzing the relation between faces at Justice and what he says now
let's see the relation for these five types of shapes.
You have a cuboid, a triangular pyramid, triangular prism, a pyramid with the square base and a prism
with a square base.
All right, let's get started and we will try to find the faces, what it says and just what each of
these not over here you have a cuboid.
So this is a quote right now.
You can see that it has six faces.
We've already seen that.
Right?
This is one.
This is two.
This is three.
And then you will have three more, which you can see from here.
And how many what is this?
Do you have we have one, two, three, four over here.
And similarly, you will have four over here also.
So that's eight what it says.
And it has 12 edges.
Right.
Your forehead just on the top or just on the bottom.
And then this is one and two.
Similarly one and two.
So four plus four plus four.
That's twelve edges.
So that's six faces, eight vertices and twelve edges.
All right.
Now let's take the same faces.
Plus what it says that six plus eight, it gives you 14.
Right.
Similarly, if you take it just plus two, that's twelve plus two.
That's also equal to fourteen.
Interesting, right?
These two values are coming as equal.
Now, let's try a triangular pyramid.
You must have seen the pyramids in Egypt, right.
So this type of shape is called the triangular pyramid, and it's called a triangular pyramid because
the base is of a shape of a triangle.
Right.
These two sides will be joined right now.
How many faces does it have?
It has one, two and three.
And the bottom.
That's four faces.
Right.
And how many bodies does it have?
It has three.
What is at the bottom and one over here.
That's four vertices.
And you can see that it has six edges, which are the six edges.
You have three at the bottom and then one, two and three over here.
The three plus three equals six.
All right.
Now let's dig phases plus what he says.
That's four plus four, which gives you eight.
And what about it?
Just plus two?
That six plus two, which gives you eight.
All right.
They're coming equal.
That's also interesting.
Now, let's take a triangular prism, OK?
This is a triangular prism over here.
You have a triangular shape and the bottom also has a triangular base.
Right.
And these sides are rectangles.
This type of a shape is called a prism.
And because the top and bottom base are in the form of a triangle, it's called a triangular prism.
All right.
Now, let's try to find a number of faces over here.
You have one, two, three, four and five.
Right.
Two at the bottom and top and then three in the sides.
So two plus three is equal to five.
So you have five faces and you can see that you have three vertices over here and three vertices over
here.
That's six what he says.
And it has nine edges.
Right.
You have three edges over here, three over here, and then one, two and three over here.
So three plus three plus three, that's nine edges.
All right.
Now let's take Frasers plus what he says.
That's five plus six, which gives you eleven.
And let's take it just plus two.
That's nine plus two, which gives you also eleven.
All right.
Now, let's go ahead with the pyramid, with the square base.
Now, imagine you had this same shape over here, but you have a square base.
All right.
Now, how many faces will it have?
It will have four plus one.
That's five faces and four vertices at the bottom and one at the top.
That's five vertices.
And it'll have eight edges.
Right, or at the bottom and four over here.
One, two, three and four.
But I love eight just right.
So phases plus what it says gives you ten.
Right.
And it just plus two.
That's eight plus two.
That also gives you ten.
All right.
Now let's check a with the square base that look like this and you can see that this is the same as
a cuboid.
Both are the same.
All right.
Now over here, this is a prism, right?
And it has a base in the shape of a square.
That's why it's called a prism with a square base.
Now, how many faces does it have?
It has six faces.
How many?
What is says one, two, three, four and four at the bottom.
That's eight what it says.
And it has 12 edges or over here or at the bottom.
And then one, two, three and one more over here.
That's four.
So four plus four plus four.
That's four twelve edges just now.
Let's take faces plus what it says that six plus eight which is equal to fourteen.
And what about it.
Just plus two.
That's twelve plus two which is also equal to fourteen.
Now this is a beautiful property which we have seen over here.
That is the number of faces plus the number of what is says is equal to the number of it just plus two.
And this is what we call the Euler's formula.
All right.
And this is true for any Hedren.
All right, now, let's take an example of a question to analyze the utility or the usefulness of this
formula.
All right.
Over here we have a question.
A politician has seven faces and 10.
What is this?
How many it just does the police have.
All right, let's get started.
Now, we know that the faces is equal to seven.
The what it says is equal to ten.
And we need to find the number of it just.
Now faces plus what he says is equal to it, just plus two as per the Oilor formula, therefore we can
solve that the number of adults will be equal to 15.
Now, let's do one more question.
The Euler's formula is true for all three dimensional shapes.
Now, is that true?
No, it's not true.
Right.
We have seen that it's true only for Poly Heidrun, right?
Not all three dimensional shapes.
Therefore, this is false.
And this formula works for all politicians except once having holes through it.
Now, don't worry, you will not be getting these type of questions.
But only headrests that have a hole through it are not simple polygons.
OK, so they are called non simple politicians.