The Most Mathematical Flag - Numberphile

Key Takeaways

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 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 flag flags and you know 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 Five of the Nepal Constitution where it describes how to construct the nation's flag uh shall I read it to you schedule one 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+ 1/3 AB from AC mark off D making a line a d equal to line AB join b d from BD mark off e making be e 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 uh for a country certainly that isn't a square or a rectangle makes it very unusual but Napal are booking 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 1/4 of line ab and starting from H draw a line hi parallel to line AC touching line CG G at point I if it was on cloth we could just like fold it in half and Mark it see so maybe I'll do that with the paper so I want to draw half this distance BCT CF at J and draw a line J K 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 J K and hi I cut one another nine join JG 10 let M be the point where line JG and hi I cut one another with Center M and with a distance shortest from M to BD Mark I can't give a great face okay 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 and on the lower portion and let p and Q be the points where it touches the line o m respectively with Center M and radius mq draw a semicircle on the lower portion touching p and Q with Center M and radius n m draw an arc touching P NQ at R and S join RS let T be the point where RS and hii 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 uh this is what it was like to the Greeks all ma 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 2 point 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 I cheated a little bit just a little bit C method of making the sun bisect line AF at U and draw line UV parallel to line AB touching line be e at V I'm gone blind ah it's like it's all swimming now okay 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's and Zeds 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 Apex 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 h i RS Fe e d JG oq JK and UV are imaginary similarly the external and internal Circles of the sun and the other arcs except the cresant moon are also imaginary these are not shown on the flag and it's as easy as it sounds for