Name: Introduction to Non-euclidean Geometry
Uploaded: 2019-07-19
Duration: 8 min 45 s
Description: In this video, we are going to learn more about Euclidean geometry and its limitations. We will also learn more about non-euclidean geometry.

Question

How would you rewrite Euclid's fifth postulate so that it would be easier to understand?

Accepted Answer

Two lines are said to be parallel if they are equidistant from one other, and they do not have any point of intersection. In order to understand it easily let us take any line $l$ and a point $P$ not on $l .$

By Play fair’s axiom (equivalent to the fifth postulate), we know that there is a unique line $m$ through $P$ which is parallel to $l .$

Now, the distance of a point from a line is the length of the perpendicular from the point to the line.

Let $A B$ be the distance of any point on $m$ from $l$ and $C D$ be the distance of any point on $l$ from $m .$

We can observe that $A B = C D .$ In this way the distance will be the same for any point on $m$ to $l$ and any point on $l$ to $m$ .

So, parallel lines are always the same distance apart.

EXERCISE

Jharkhand Board Mathematics Solutions for EXERCISE

Questions from EXERCISE with Hints & Solutions

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