Question

I want to understand the Zenon's paradox. Does the rabbit gets to its to the goal?

Answer 1

Yes he does
and it's Zeno's paradox

Answer 2

Depending on the version you are looking at the wording may change, but it still winds up as the sum of half the remaining distance plus half the remaining distance....
which can be written as a summation formula.
say the distance to be covered is 1
then first the rabbit travels half the distance so 1/2
then he travels half the remaining distance so 1/2+1/4
another half is
1/2+1/4+1/8...
the patter continues...

Answer 3

But How could that happened?. He is always half the distance!

Answer 4

watch the pattern of distances travelled

Answer 5

1/2+1/4+1/8+1/16+...

this can be written as\[\sum_{n=1}^{\infty}(\frac{1}{2})^n\]it can be shown that this sum converges to exactly 1:\[\sum_{n=1}^{\infty}(\frac{1}{2})^n=1\]hence the rabbit gets where it is going, because it travels the distance in question: 1

Answer 6

don't believe me that the series converges?
Study up on geometric series and you will see.

Answer 7

use pie chart to see that it converge

Answer 8

Yeah, the problem here, is that I don't understand quite good the infinity

Answer 9

A pie chart?

Answer 10

never seen that before
go ahead imran

Answer 11

You mean split the pie chart by a half every time?

Answer 12

yes

Answer 13

if you keep going, you would have filled the whole chart

Answer 14

plus...

Answer 15

But I can't do that at constant velocity haha

Answer 16

plus..

Answer 17

half and half and half...

Answer 18

But, it's very interesting, I will try it at launch!