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National Flag of Nepal | Maths Behind world’s unique flag

The Amazing National Flag of Nepal | Maths Behind the world's unique flag

Nepal has stayed a distinct, independent country, and its traditional flag, whose simple style dates back centuries, flies with pride. Crimson is the background color, dark blue is the border — both are common colors in Nepalese art and decoration. A white moon displaying eight rays in the upper segment, with a crescent added below; a white, stylized sun with 12 rays emerges in the bottom segment. Furthermore, the given methods are adopted from the Constitution of Nepal, Article 5.

Such two icons are linked to various dynasties and both reflect the expectation that the nation will have the same longevity as the sun and moon. Even when the new constitution of December 16, 1962. these features remain the same and the symbols appear on the dozens of different civil and military flags used by Nepalese officials. Meanwhile, this article is based on explaining step by step method of making Nepali flag. And in the end, you will realize the exceptional mathematics behind the making these flags.

The Amazing National Flag of Nepal | Maths Behind the world's unique flag

Method of making the shape inside the border

  • On the lower portion of a crimson cloth draw line AB of the required length from left to right.
  • From A draw a line AC perpendicular to AB making AC equal to AB plus one third AB.
  • From AC mark off D making line AD equal to line AB. Join B and D. From BD mark off E making BE equal to AB.
  • 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.
  • Join C and G.

Method of making the moon

  • From AB mark off AN 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.
  • Bisect CF at J and draw a fine JK parallel to AB touching CG at point K
  • Let L be the point where lines JK and HI cut one another.
  • Join J and G.
  • Let M be the point where line JG and HI cut one another.
  • With centre, M and with a distance shortest from M and BD mark off N on the lower portion of line HI.
  • Touching M and starting from 0, a point on AC, draw a line from left to right parallel to AB.
  • With centre L and radius LN draw a semi-circle on the lower portion and let P and Q be the points where it touches the fine OM respectively.
  • With centre M and radius MQ draw a semi-circle on the lower portion touching P and Q.
  • With centre 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.
  • With centre T and radius TS draw a semi-circle on the upper portion of PNQ touching it at two points.
  • With centre T and radius TM draw an arc on the upper portion of PNQ touching at two point.
  • Eight equal and similar triangles of the moon are to be made in the space lying inside the semicircle of No. and outside the arc of No.

Method of making the sun

Bisect line AF at U, and draw a line UV parallel to AB line touching line BE at V.
With centre W, the point where HI and UV cut one another and radius MN draw a circle.
With centre W and radius LN draw a circle.
Twelve equal and similar triangles of the sun are to be made in the space enclosed by the circles of No.
with the two apexes of two triangles touching line HI.

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 prodded on all the sides of the flag. However, on the five angles of the flag the external angles are equal to the internal angles.

Cambridge Mathematician, DR.James Grime explaining and showing a demo of making Nepal’s Flag.

The above-mentioned border will be provided if the falg is to be used with a rope. On the other hand, if it is to be hoisted on a pole, the hole on the border on the side AC can be extended according to requirements. The lines HI, RS, FE, ED, JG, OQ, JK and 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.

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Written by Vineet

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