Question

what is eular formula? in which branch of math is it used

Answer 1

hii!!

Euler's formula is a formula to verify whether the polyhedron is possible or not by the given no. of faces, vertices and edges.

it is also used when we have to find the no. of faces, vertices or edges.

EULER'S FORMULA IS F+V-E=2

★ let me give u some examples.

=> verify whether the polyhedron is possible or not with the given no. of faces, vertices and edges.

faces=6
vertices=8
edges=12

verification:-

F+V-E=2

=(6+8)-12
=14-12
=2

HENCE VERIFIED

THUS THIS POLYHEDRON IS POSSIBLE

=> given:-

faces=9
vertices=10
edges=6

F+V-E=2

=(9+10)-6
=19-6
=13

HENCE NOT VERIFIED

THIS IS NOT POSSIBLE.

now we will find how to find faces or vertices or edges.

=> given:-

faces=?
vertices=5
edges=8

we know that=F+V-E=2

→ F+5-8=2
→ F+(-3)=2
→ F-3=2
→ F=2+3
→ F=5

verification:-

F+V-E=2

=(5+5)-8
=10-8
=2

VERIFIED...

HENCE THE NUMBER OF FACES IS 5.

u can also use this formula for finding the no. of edges and vertices like how I found the no. of faces. just put the other value of face and edge or vertices and then find.

hope u understood....!

Answer 2

Euler's formula is the method which helps us to check whether the sides of the figure are right or wrong. It is mostly used in prism and etc.
Euler's formula = F+V-E