00:01
Hi, here for the given question, we need to identify the surface given by the planar model with the boundary word abca -1 dbc -1 by two methods using first one is euler characteristic and orientability of the surface and the second one is by cutting and pasting the radius to standard form.
00:29
So here first one by euler's characteristic and orientation of the surface method.
00:55
So here in our case now by euler's method as we can see that here we have four vertices a, b, c, d.
01:05
Here ages e equals to 6, ab, bc, cd, da, a inverse and c inverse.
01:16
Now faces f is equal to 2 inside the loop and one is outside the loop outside the loop comma inside the loop.
01:29
So here by using euler's formula, we can calculate the characteristic x is equal to v minus e plus f.
01:40
So x is equal to 4 minus 6 plus 2.
01:43
So here this is implies x is equal to 0.
01:47
So here for the first one, we can say that here in our case now using this we have characteristic x equals to 0.
01:55
Now further we need to calculate what is the value of orientability.
01:59
Now as we know that euler's characteristic x is equal to 0 then the surface is non -orientable.
02:20
Now by using cutting and pasting to reduce standard form method by cutting and pasting to reduce to a standard form...