Uploaded by jpmorganjr on 19.06.2011

Transcript:

BRADY HARAN: I'm in the middle of London on Regent Street--

in case you couldn't tell with all those red buses going by.

We want to talk about something

a little bit Olympics.

We're going to talk to you about flags.

There's loads of flags up the street there, but we want to

talk about one in particular.

It's one you don't often see at the Games, because, well,

this country's never actually won a medal.

But their flag?

Very mathematical.

DR. JAMES GRIME: We got chatting about countries and

their flags and things.

And I thought, well, what sort of maths

could we do with that?

And we could look at the symmetry of flags and which

has the most symmetrical flag.

Then I thought, no.

I know what the most mathematical flag is.

And this is amazing.

So Nepal, I reckon, has the most mathematical flag-- the

country of Nepal.

Because the mathematical construction for the flag is

actually written into their constitution.

And I've got it here.

This is Article 5 of the Nepal Constitution, where it

describes how to construct the nation's flag.

Shall I read it to you?

Schedule 1, relating to Article 5.

National flag.

A, method of making the shape inside the border.

One, on the lower portion of a crimson cloth, draw a line AB

of the required length from left to right.

Two, from A draw a line AC perpendicular to AB, making AC

equal to AB plus one third AB.

From AC, mark off D, making a line AD equal to line AB.

Join BD.

From BD, mark off E, making BE equal to AB.

Four, touching E, draw a line FG starting from the point F

on line AC parallel to AB to the right-hand side.

Mark off FG equal to AB.

Five, join CG.

I believe it is the only flag for a country, certainly, that

isn't a square or a rectangle.

It makes it very unusual that Nepal are bucking the trend.

They're sticking with it.

This is their flag.

And they're sticking with it.

From AB, mark off AH, making AH equal to one

fourth of line AB.

And starting from H, draw a line HI parallel to line AC,

touching line CG at point I. If it was on cloth, we could

just fold it in half and mark it, you see?

So maybe I'll do that with the paper.

So I want to draw half this distance.

Bisect CF at J and draw a line JK parallel to AB, touching CG

at point K. It is not necessary to have to measure

with your ruler.

You can follow these instructions without any

measuring at all.

It's telling you to divide things by half and quarters

and thirds.

And using those rules, without measuring, we should be able

to do this.

Let L be the point where lines JK and HI cut one another.

Nine, join JG.

10, let M be the point where line JG

and HI cut one another.

With center M and with a distance shortest from M to

BD, mark off--

I can't keep a straight face.

OK.

With center M and with a distance shortest from M to

BD, mark off N to the lower portion of line HI.

Touching M and starting from O, a point on AC, draw a line

from left to right parallel to AB.

With center L and radius LN, draw a semicircle on the lower

portion and let P and Q be the points where it touches the

line OM respectively.

With center M and radius MQ, draw a semicircle on the lower

portion touching P and Q. With center N and radius NM, draw

an arc touching PNQ at R and S. Join RS.

Let T be the point where RS and HI cut one another.

16, with center T and radius TS, draw a semicircle on the

upper portion of PNQ, touching it at two points.

This is what mathematics was like in ancient times.

This is what it was like to the Greeks.

All Greek mathematics was like this and

written down like this.

With center T and radius TM, draw an arc on the upper

portion of PNQ, touching at two points.

Eight equal and similar triangles of the moon are to

be made in the space lying inside the semicircle of

number 16 and outside the arc of number 17 of this schedule.

I made that bit up.

(WHISPERING) I cheated there a little bit.

Just a little bit.

C, method of making the sun.

Bisect line AF at U and draw a line UV parallel to line AB,

touching line BE at V. I've gone blind.

Oh, it's all swimming now.

OK.

With center W, the point where HI and UV cut one another, and

radius MN draw a circle.

Got to W. There isn't any X and Z, so yes,

we're nearly there.

It took that many letters, though.

It took nearly the whole alphabet.

Just be glad there aren't 27 steps.

What we would have done then.

With center W and radius LN, draw a circle.

12 equal and similar triangles of the sun are to be made in

the space enclosed by the circles of number 20 and of

number 21 and with the two apexes of two triangles

touching line HI.

D, method of making the border.

The width of the border will be equal to the width of TN.

This will be of deep blue color and will be provided on

all sides of the flag.

However, on the five angles of the flag, the external angles

will be equal to the internal angles.

Explanation--

the lines HI, RS, FE, ED, JG, OQ, JK, UV are imaginary.

Similarly, the external and internal circles of the sun

and the other arcs, except the crescent

moon, are also imaginary.

These are not shown on the flag.

And it's as easy as it sounds.