Maths Circumference

Maths is Fun – Circumference

00:00:06:28    This week on maths is fun, I want to talk about some maths that’s a little bit counterintuitive,

00:00:11:29     but it’s absolutely correct, Here we’ve got a globe, G’Day Australia!

00:00:16:28    So we have a bit of cable here

00:00:19:27    now if I wrap around the globe

00:00:27:26    will be the circumference.

00:00:32:25    So there it is,

00:00:35:26    wrap around nicely around the globe. See,

00:00:40:25    that fits,

00:00:41:24    so I wrap a cable around.

00:00:44:24    Now, if I wanted this cable to hover,

00:00:50:23    one inch above the earth, all I would need to do roughly is add

00:00:58:22    six inches of the cable.

00:01:03:21    And then they haven’t, I’ve got a cable that will wrap

00:01:07:20    that will be an inch

00:01:08:19    So here’s where the

00:01:18:18    bit comes in. That doesn’t sound very intuitive.

00:01:21:17    Because

00:01:23:16    that’s clear that I just added that much cable to this cable here, right.

00:01:27:15    And we got an inch around an inch above there.

00:01:30:14    anything except for that, that seems right, given the size of that globe.

00:01:34:13    Here’s the trick.

00:01:36:12    If I did the same thing with Planet Earth,

00:01:39:11    so imagine that I had a cable wrap tightly around all of Earth. Now Earth is about 24,900 miles,

00:01:49:10    miles around it’s huge.

00:01:52:09    If I wrapped the cable tightly around that, so my cable was 24,900 miles long,

00:01:59:08    if I added just six inches to that cable,

00:02:03:07    I would be able to lift that cable off the ground all the way around the Earth by just under an inch.

00:02:10:06    Actually point nine five an inch if you want to get precise, but roughly an inch

00:02:16:05    or let’s look at it a bit different.

00:02:19:04    This is a six-foot cable here.

00:02:22:03    If I added this six-foot cable to my cable that is 24,900 miles long

00:02:32:02    and wrapped around the Earth, that cable would sit a whole foot

00:02:37:01    above the earth all the way around.

00:02:41:00    So why does that work that seems bananas that a cable, this long

00:02:46:29    added to a cable that is 24,900 miles long,

00:02:51:28    we have the effect of lifting by a foot all the way around. That just doesn’t sound right.

00:02:58:27    But it is because of maths.

00:03:01:26    So how it works is this.

00:03:03:25    The circumference is two times pi times the radius.

00:03:12:24    So if you think about it, then the Earth’s radius is 3958 miles give or take.

00:03:22:23    And that’s why when we times that by two pi, we get our circumference, which is 24,900.

00:03:29:22    But if we add another

00:03:33:21    bit of distance, if we say we want one more foot

00:03:35:20    Well, if we took that one foot and times that by two pi

00:03:39:19    and added that to the to the formula, you get a new a new number.

00:03:44:18    So whatever you want to add just times by two pi

00:03:47:17    now pi is 3.14159, whatever the big long number, but let’s say it’s 3.14.

00:03:57:16    That means if I’m going to time something by two, I’m going to times it by 6.28.

00:04:03:15    So hence that if I take my six feet,

00:04:06:14    and I divided by two pi or 6.28, I’m left with just under one foot

00:04:15:13    So that’s why the matter works.

00:04:17:12    So in any object is the same whether you’re talking about the globe, a basketball, a giant sphere, earth, an entire galaxy doesn’t matter.

00:04:27:11    If you add something more,

00:04:32:10    it will have the effect of making a bigger circle

00:04:38:09    that is almost exactly one six, smaller than the bit you added.

00:04:43:08    So in this instance, I added six inches to my cable

00:04:49:07     and that had the effect of adding an inch all the way around.

00:04:53:06    If you had six feet, add just under one foot and so on and so forth. Amazing