Verify the relationship V + E - F = 0 for the five regular polyhedra, where V is the number of vertices, E is the number of edges and F is the number of faces.
uler’s formula is a statement about convex polyhedra, that is a solid whose surface consists of polygons, called its faces, such that any side of a face lies on precisely one other face, and such that for any two points on the solid, the straight line connecting them lies entirely within the solid. Each convex polyhedron carries with it certain data, for example the number of faces F, the number of edges E, and the number of vertices V. Euler’s formula gives a relationship between these data, namely
V-E+F=2
for all convex polyhedra. The idea that this specific alternating sum should remain constant no matter what convex polyhedron you feed it is not at all clear. We will try to prove it by induction, the obvious question being induction on what? To answer that we first make a cute observation. We can transfer these data relating to our polyhedron into some data about a connected graph in a simple way. To see how lets look at the example of a cube.
If you imagine peering through one of the faces like a window and tracing out what you see you might end up with something like this:
The important observation is that this is a connected plane graph which has the same number of edges and vertices as the cube, and one fewer face (we lose the face that we were peering through). We can see that in fact this is the case for all convex polyhedra. In this way we
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Find the point on the x-axis which is equidistant from (3,2) and (-5,-20)
Perform the following steps listed below and check whether the answer is a multiple of 9?
Step-1 Choose a number between 100 and 1000
Step-2 Interchange its first and last digits to make another number
Step-3 Subtract the small number from the largest number
Step-4 Repeat step-2 for the number obtained in step-3
Step-5 Now add the numbers obtained in step-3 and step-4.
Try with some other starting number between 100 and 1000 and check whether the answer is a again a multiple of 9.
A Tangram is a shape that is divided into different pieces, which can then be rearranged to make lots of shapes. The first tangram was invented in china and is as given below:
Identify the quadrilaterals and triangles in the shape and name the type of each one, Create another shape using the different pieces given in the given shape following the rule: Whole side must match whole sides with edges meeting each other.
Simplify the following
The mirror image in the following case in
If a = 14 ,b = 40 ,c = 04 and d = 41, then
1) a = b 2) b = c
3) a = c 4) a = d
[(- 2)(-2) ](-3) is equal to
1) 64 2)
3) - 64 4)