All Object Lessons
Belief & Identity

The Flag of Nepal: The Only Flag That Is Not a Rectangle

⏱ 45 minutes 🎓 Primary & Secondary 📚 history, mathematics, art, ethics, citizenship
Core question Why is one country's flag a different shape from every other country's flag — and what does that difference say about the country, its history, and the choices a people can make about how to represent themselves?
The flag of Nepal — the only non-rectangular national flag in the world. The exact shape is described by a 24-step mathematical construction in the Constitution of Nepal. Photo: Drawn by Pumbaa80, Achim1999 / Wikimedia Commons / Public Domain
Introduction

Every country in the world has a flag. Almost every flag is a rectangle. Most are wider than they are tall. The shape is so standard that it goes almost unnoticed. Look at any flag — the United States, China, India, Mexico, France, Brazil — and you will see the same shape: four right angles, two long sides, two short sides. Then look at the flag of Nepal. Nepal's flag is not a rectangle. It is two triangles, one on top of the other, sharing the same left edge. The top triangle is smaller. The bottom triangle is larger. Both are deep red, with a blue border running along every outside edge. Inside the top triangle is a white crescent moon. Inside the bottom is a white sun. The flag has five corners. It is the only non-rectangular national flag in the world. It is also the only one that is taller than it is wide. The shape is not an accident, and it is not new. South Asian rulers have used triangular pennants for over a thousand years. Hindu temples often fly triangular flags. The kings of Nepal used two separate triangular pennants for different branches of the ruling dynasty. In 1962, when Nepal adopted a new constitution, the two pennants were combined into one flag, and the exact shape was defined mathematically in Schedule 1 of the Constitution — 24 steps of geometry, anyone with a ruler and a compass can follow. Nepal kept this same shape into its 2015 Constitution. While every other country adopted the European rectangular flag, Nepal kept its own. This lesson asks why Nepal made a different choice, what the flag means, and what it teaches about how a country can be itself even when the rest of the world has agreed on something else.

The object
Origin
Nepal. The double-pennon shape comes from much older triangular flags used by South Asian rulers, temples, and military units for over a thousand years. The modern standardised version was adopted in 1962.
Period
Triangular pennants have been used in Nepal and the wider Indian subcontinent for over a thousand years. The double-pennon design of two stacked triangles became standard after the unification of Nepal by King Prithvi Narayan Shah in the 1760s. The exact modern flag was standardised by Schedule 1 of the Constitution of the Kingdom of Nepal, adopted on 16 December 1962. The same standard was kept in the Constitution of Nepal, 2015.
Made of
Cloth. Traditionally cotton, now often polyester for durability. Crimson red for the two triangles, deep blue for the border, white for the moon and sun emblems. The shape is precise, the colours are specified.
Size
Any size, but always with the same proportions. The ratio of height to longest width is an irrational number (the smallest root of a quartic polynomial), not a simple fraction. The flag at any size must follow the 24-step geometric construction in the Constitution.
Number of objects
Many millions of Nepalese flags are in use, in Nepal and in Nepalese communities worldwide. Every government building, every embassy, many schools, homes, and businesses fly one. The flag is also stitched into clothing, prayer flags, and ceremonial decorations.
Where it is now
Throughout Nepal, in Nepalese embassies worldwide, and in Nepalese diaspora communities (about 4 to 5 million Nepalese live outside Nepal). The flag has flown on Mount Everest, on the Burj Khalifa in Dubai, and on a stamp issued by Israel.
Before you teach this — reflect

Questions for you

  1. Nepal is a real living country with a complex modern history. How will you teach the flag as a real political symbol, not as a curiosity?
  2. Nepal is religiously diverse (mostly Hindu, with significant Buddhist and other communities). How will you handle the flag's religious symbolism with care?
  3. Nepal has been through major political changes recently (becoming a federal democratic republic in 2008). How will you mention this without going too deep into adult politics?

Common student difficulties — tick any you have noticed

Discovery sequence
1
Look at the flags of the world. The United Nations recognises 193 member states. 192 of them have rectangular national flags (or square, in the case of Switzerland and the Vatican). One does not. That one is Nepal. The rectangular flag was not the first design used by humans. People in many parts of the world used triangular pennants, square banners, swallowtail flags (with split ends), and many other shapes for centuries. The rectangular flag became standard in Europe in the late Middle Ages, and from there spread to most of the world through European empires. Nepal never adopted it. Why might Nepal be the only country with a different shape?
Points to consider (for the teacher)

Because Nepal was never colonised. Most countries adopted European-style rectangular flags either during colonial rule or after independence, often based on flags designed during colonial times. Nepal was never part of the British Empire, even though Britain ruled almost all of South Asia. The Anglo-Nepalese War of 1814-1816 ended with a treaty that left Nepal independent, though smaller. Nepal kept its own kings, its own laws, its own customs, and its own flag. By the time European-style rectangular flags became the world standard, Nepal already had its own tradition and saw no reason to change. The two-pennant design came from the kings of Nepal — one pennant for the senior branch of the ruling family, one for the junior branch (the Ranas, who ruled as hereditary prime ministers from 1846 to 1951). When the country was unified, the pennants were combined. When the modern constitution was written in 1962, the design was kept. Students should see that 'global standard' is often the result of historical power — European empires set the standards, and most countries inherited them. Nepal kept its own way because it was free to keep its own way. The flag is a daily reminder of a country that was never told what shape its symbol should be.

2
The flag is full of meaning. Each part has its symbolism, layered through centuries. The two triangles. Some say they represent the Himalayan mountains, which dominate Nepal's landscape and include Mount Everest. Some say they represent the two main religions of Nepal, Hinduism and Buddhism, both with deep roots in the country. Some say they come from the two branches of the ruling dynasty. All of these readings are present in Nepalese tradition. The crimson red. Nepal's national colour. The colour of the rhododendron, Nepal's national flower. Also the colour of bravery — the Gurkha soldiers of Nepal are famous worldwide for their courage in battle. The deep blue border. Peace and harmony. The colour of the sky above the mountains. The sun in the lower triangle. Twelve rays. Represents the warmth and the determination of the Nepalese people. Some say it also represents the hot southern lowlands (called the Terai). The moon in the upper triangle. Eight rays visible (out of sixteen). Represents the calmness and the spiritual nature of the Nepalese people. Some say it also represents the cool mountain regions. Together, the sun and the moon say something specific: as long as the sun and moon last, Nepal will last. What does it mean for a flag to carry so many meanings?
Points to consider (for the teacher)

That a flag, like a language, accumulates meaning over centuries. Each generation adds its readings. The Himalayas, the religions, the dynasties, the rhododendron, the bravery, the eternal life of the nation — all of these are present at once. A Nepalese person looking at the flag may think of one or several of these at any moment. The flag is not a single picture but a small library of meanings. This is true of most national flags, but few have as many layers as Nepal's. Some flags are simply abstract designs (the three horizontal stripes of many countries). Some have one strong symbol (the star and crescent of Turkey). Nepal's flag has at least seven distinct symbolic elements, each with its own history. Students should see that 'a flag is just a piece of cloth' is wrong. A flag is a compressed story. The story of Nepal is compressed into a piece of cloth that takes a particular shape and carries particular symbols, and every Nepalese person learns to read it.

3
Nepal's flag is not just designed. It is constructed — mathematically. Schedule 1 of the Constitution of Nepal contains 24 specific geometric steps to draw the flag exactly. The instructions use lines, perpendiculars, arcs, and circles. Anyone with a ruler and a compass can follow them. The result is a flag in precise proportions, the same everywhere. The basic instructions begin: 'On the lower portion of a crimson red cloth, draw a 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...' and so on, for 24 numbered steps. The sun is constructed from circles. The moon is constructed from semi-circles. The border is exactly the width of one specific measurement. The angles are precise. The ratio of the flag's height to its widest width is an irrational number — meaning it cannot be written as a simple fraction. It is the smallest root of a fourth-degree polynomial equation. This means Nepal's flag has the most mathematically precise definition of any national flag in the world. Most other flags are described by simple ratios like 2:3 or 1:2. Nepal's is described by equations. Why might a country put geometry into its constitution?
Points to consider (for the teacher)

Because they wanted to be precise. The history of the Nepalese flag includes many slightly different drawings — different angles, different proportions, different sun rays, different moon shapes. By 1962, the king and government wanted one official version that everyone would use, and they wanted it to be unambiguous. So they wrote out the geometry. Mathematics is a way of saying things exactly, without arguments about interpretation. Once the construction is in the Constitution, no one can draw the flag wrong and call it official. Many countries also have flag specifications, but Nepal's is unusually thorough. The 24 steps cover everything from the basic shape to the exact pattern of the sun's rays. Students should see that constitutions can contain unexpected things. Most constitutions talk about laws, rights, and government structures. Nepal's constitution also includes geometry lessons. This is not strange — it shows what mattered enough to write into the basic law of the country. Nepal cared enough about its flag to make it mathematically permanent.

4
The flag has been through political change. In 1962, when the current design was standardised, Nepal was a kingdom. The flag was tied to King Mahendra, who had taken power in a 1960 coup that ended Nepal's first experiment with democracy. The flag's symbolism was officially tied to the monarchy and to Hinduism, which was the state religion. Nepal changed. A democratic movement in 1990 forced the king to share power. A long civil war (1996-2006) led by Maoist rebels reshaped politics. In 2006, the king lost most of his powers. In 2008, the monarchy was abolished entirely, and Nepal became a federal democratic republic. In 2015, a new constitution was written and approved. The new constitution kept the same flag. Some people argued for change. The flag's links to monarchy and to Hinduism, some said, did not fit a republic with many religions. Maoists, secularists, and some ethnic groups proposed new designs. The proposals were rejected. The 2015 Constitution kept the same 24 steps of geometry, the same crimson and blue and white, the same sun and moon. Schedule 1 of the new Constitution is, in this matter, identical to Schedule 1 of the old one. What does it mean to keep a flag through such big changes?
Points to consider (for the teacher)

That the flag had become more than a royal symbol. Even people who opposed the monarchy mostly agreed that the flag belonged to all Nepalese, not just to the kings. The double-pennon design predates the modern monarchy by centuries. The two triangles, the sun, the moon — these are older than any one dynasty or any one government. To keep the flag was to say: Nepal continues. The political system has changed. The country has not. This is unusual. Many countries change their flags when their governments change. Russia changed its flag with the fall of the Soviet Union. South Africa changed its flag with the end of apartheid. Some Nepalese said theirs should change too. The decision to keep it shows that, in Nepal, the flag had become a symbol of the country itself rather than of any particular government. Students should see that flags can outlast governments, and that the choice to keep or change a flag is a serious political decision. Nepal made the choice to keep. The country flies today, in 2026, the same flag it flew in 1962, even though almost everything else about how Nepal is governed has changed.

What this object teaches

The flag of Nepal is the only non-rectangular national flag in the world. It is also the only one taller than wide. The flag has five corners — two stacked triangular pennants, the smaller on top, sharing the same left edge. Both triangles are crimson red, with a deep blue border. The upper triangle contains a white crescent moon with rays; the lower triangle contains a white sun with twelve rays. The double-pennon design comes from much older triangular flags used by South Asian rulers and temples for over a thousand years. The two triangles originally represented two branches of Nepal's ruling dynasty, joined into one flag after the country was unified by King Prithvi Narayan Shah in the 1760s. The exact modern flag was standardised on 16 December 1962, when civil engineer Shankar Nath Rimal designed it on the request of King Mahendra. Schedule 1 of the 1962 Constitution included a 24-step geometric construction for the flag — and the same construction was kept in the 2015 Constitution, after Nepal became a federal democratic republic. The flag survived the abolition of the monarchy and a major civil war. The flag's symbolism includes the Himalayas, the bravery of the Nepalese people (the colour red), peace (the blue border), the eternal existence of Nepal (the sun and moon), and the country's two main religions (Hinduism and Buddhism). Nepal was never colonised by a European power, and its flag is one of the most visible reminders that the global standard of rectangular flags is itself a product of European history.

QuestionMost national flagsThe Nepalese flag
What shape is it?A rectangle (or sometimes a square)Two stacked triangles — a five-cornered shape
How wide vs how tall?Usually wider than tall (ratio like 2:3 or 1:2)Taller than wide (the only national flag like this)
How is the shape defined?Usually by a simple ratioBy 24 specific geometric construction steps in the Constitution
Where does the shape come from?Mostly from European flag traditionsFrom South Asian triangular pennants over a thousand years old
Has the shape changed in modern times?Many countries have changed their flagsThe same flag has been used continuously since 1962, kept by every constitution since
Why this shape?Because the country adopted the European standardBecause Nepal was never colonised and kept its own tradition
Key words
Double-pennon
The two-triangle shape of the Nepalese flag. Two triangular pennants stacked, sharing the same left edge. Comes from older South Asian triangular flags used by rulers, temples, and military units.
Example: The two pennants originally represented two branches of Nepal's ruling dynasty — the senior royal line and the Rana branch that served as hereditary prime ministers from 1846 to 1951.
Schedule 1 (of the Constitution of Nepal)
The section of Nepal's Constitution that describes the national flag, including the 24-step geometric construction. Included in both the 1962 Constitution and the 2015 Constitution. The instructions are identical.
Example: The instructions begin: 'On the lower portion of a crimson red cloth draw a 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...'
King Mahendra
King of Nepal from 1955 to 1972. In 1962, he introduced a new constitution that included the standardised flag design. Mahendra was also responsible for many other modernising reforms, though his rule was authoritarian.
Example: Mahendra commissioned civil engineer Shankar Nath Rimal to design the precise geometric construction of the flag. Rimal's design is what appears in every Nepalese constitution since 1962.
Sun and moon
The two white emblems in the flag. The sun (12 rays) in the lower triangle. The moon (a crescent with 8 visible rays, of 16 implied) in the upper triangle. Together they symbolise the eternal existence of Nepal — as long as the sun and moon last, Nepal will last.
Example: Before 1962, both the sun and moon on the flag had human faces. The faces were removed in the 1962 modernisation to give a simpler look while keeping the meaning.
Crimson red (Nepal Red)
The deep red colour of the flag's two triangles. The national colour of Nepal. Also the colour of the rhododendron, Nepal's national flower, and traditionally associated with bravery, victory, and celebration in Nepalese culture.
Example: The Gurkha soldiers of Nepal, famous for their bravery, are sometimes called 'the men of crimson' in poetic references to the national colour.
Federal democratic republic
The form of government Nepal adopted in 2008, after abolishing the monarchy. Nepal is now governed by an elected parliament and a president. The transition involved a long process of constitutional reform that produced the 2015 Constitution.
Example: Despite this huge change in government, the Constitution of 2015 kept the same flag as the Constitution of 1962. The flag survived the end of the monarchy.
Use this in other subjects
  • Mathematics: The Nepalese flag is defined by 24 geometric construction steps. Try drawing the flag using only a ruler and a compass. The flag's height-to-width ratio is an irrational number — the smallest root of a quartic polynomial. Discuss: most national flags use simple ratios like 2:3, but Nepal's uses geometry that requires construction. This is a real example of mathematics in public life.
  • Geography: On a map of Asia, locate Nepal, between India and China, in the Himalayas. Mark Mount Everest (Sagarmatha in Nepali), the world's highest mountain, on the border between Nepal and Tibet (China). Discuss how Nepal's geography — high mountains, narrow valleys — affected its history. The same geography that protected Nepal from colonisation may have helped it keep its unique flag.
  • History: Build a timeline of Nepal: ancient triangular pennants in South Asia (over 1,000 years), unification of Nepal by Prithvi Narayan Shah (1768), Anglo-Nepalese War (1814-1816) ending in Nepal's preserved independence, Rana rule (1846-1951), monarchy restored (1951), Constitution and standardised flag (1962), democratic movement (1990), civil war (1996-2006), monarchy abolished (2008), new constitution kept the same flag (2015). The flag has flown through all of these changes.
  • Citizenship: Nepal kept its flag through major political changes — including the end of the monarchy. Discuss: what makes a national symbol last? Why might citizens want to keep a flag from a previous government? Other examples include the French tricolour (used by monarchies, republics, empires, and the current Fifth Republic) and the US flag (used through huge changes in American history).
  • Art: Compare the Nepalese flag to other unusual flags. The Swiss flag is a square. The Vatican flag is a square. The Ohio state flag in the United States is a swallowtail (not a rectangle). Discuss: what makes a 'normal' flag shape? Where did the standard come from? Students design their own flag in a non-rectangular shape, reflecting something they value.
  • Ethics: Nepal's flag has religious symbolism (Hindu and Buddhist). When Nepal became a secular republic in 2008, some argued the flag should change. Discuss: should national symbols change with the government, or should they outlast governments? Both arguments are real. Strong answers will see that there is no easy right answer.
Common misconceptions
Wrong

Nepal's flag is a recent invention to be different from other countries.

Right

The double-pennon design comes from triangular flags used in South Asia for over a thousand years. Nepal kept the older tradition while other countries adopted European-style rectangles. The shape is older than most modern national flags.

Why

Calling it 'recent' makes it sound like a gimmick. The truth is that Nepal's flag is one of the oldest continuously-used designs in the world.

Wrong

Nepal was once part of the British Empire like India.

Right

Nepal was never colonised by Britain or any other European power. The Anglo-Nepalese War of 1814-1816 ended with a treaty that left Nepal independent (though it lost some territory). This independence is one reason Nepal kept its own flag traditions instead of adopting European ones.

Why

People often assume all South Asian countries shared the same colonial history. Nepal and Bhutan were exceptions.

Wrong

The mathematical construction of the flag is just for show.

Right

The 24-step geometric construction is the legal definition of the flag in the Constitution. It exists because earlier versions of the flag were drawn slightly differently in different places, and the government wanted one official, precisely defined version. Mathematics is a way of being legally exact.

Why

This is a real example of how mathematics is used in law and public life — not just an abstract academic subject.

Wrong

When Nepal became a republic in 2008, it got a new flag.

Right

Nepal kept the same flag through the abolition of the monarchy and the writing of a new constitution in 2015. Some people argued for a new design, but the proposals were rejected. The flag survived a huge change in government.

Why

Most people assume political change means new symbols. The Nepalese case shows that sometimes a flag can outlast the system that first standardised it.

Teaching this with care

Treat Nepal as a real living country with a complex modern history, not as an exotic mountain kingdom from a tourism brochure. The country is officially the Federal Democratic Republic of Nepal. Use the country name 'Nepal' (pronounced roughly 'neh-PAHL' with stress on the second syllable, not 'NEE-pul'). Nepal has about 30 million people, with many ethnic groups and languages. The official language is Nepali, written in the Devanagari script. Nepal is religiously diverse. Most Nepalese (about 81 percent) are Hindu. About 9 percent are Buddhist, including the strong Tibetan Buddhist tradition in the high mountain regions. There are also significant Muslim, Kirat (indigenous), and Christian minorities. Treat all of these with respect. The flag's religious symbolism (Hindu and Buddhist) is one reason some Nepalese citizens have argued for change. Mention this fairly without taking a side. Avoid the lazy 'Mount Everest country' framing. Nepal has Mount Everest, but it is also a country of cities (Kathmandu has over a million people), of diverse cultures, and of complex politics. Many modern Nepalese live in cities, work in offices, and have nothing to do with mountaineering. Be sensitive about the monarchy. King Birendra and most of the royal family were killed in a massacre in the royal palace in 2001, an event that remains officially unexplained. Mention the monarchy's end factually (abolished in 2008), but do not dwell on the violent moments. Be careful with the civil war (1996-2006). About 17,000 people died. The conflict is recent and many Nepalese have personal memories of it. Mention it briefly and respectfully, without graphic detail. Many Nepalese live outside Nepal (about 4 to 5 million in the diaspora). They are spread across India, the Gulf states, Malaysia, the United Kingdom, the United States, and many other places. The flag flies in many countries. If you have students of Nepalese heritage, give them space to share but do not put them on the spot. Finally, end the lesson on the present. The flag flies today, in 2026, over a country that is finding its way as a young republic. The story is not closed.

Check what students have understood

Answer each question in one or two sentences. Use what you have learned about the Nepalese flag.

  1. What makes the Nepalese flag unique among national flags?

    It is the only national flag in the world that is not a rectangle (or square). It is also the only national flag that is taller than it is wide. It is shaped like two stacked triangles, sharing the same left edge.
    Marking note: Award full marks for any answer that recognises the non-rectangular shape. Mentioning the taller-than-wide detail is a bonus.
  2. Why is Nepal's flag a different shape from other countries' flags?

    Because Nepal was never colonised by a European power. Most countries adopted European-style rectangular flags during or after colonial rule. Nepal kept its older South Asian tradition of triangular pennants, which had been used in the region for over a thousand years.
    Marking note: Strong answers will mention both the non-colonisation and the older tradition. Either alone earns most marks.
  3. What does the flag show, and what does it mean?

    The flag is two crimson red triangles with a deep blue border. The upper triangle contains a white crescent moon. The lower triangle contains a white sun with 12 rays. Together, the sun and moon symbolise that Nepal will last as long as the sun and moon last. The triangles also represent the Himalayas and Nepal's two main religions (Hinduism and Buddhism).
    Marking note: Award full marks for any answer that mentions the colours, the sun and moon, and at least one symbolic meaning.
  4. How is the flag legally defined?

    By 24 specific geometric steps in Schedule 1 of the Constitution of Nepal. Anyone with a ruler and compass can follow the steps. The result is a flag in precise proportions, the same everywhere. The ratio of height to width is an irrational number — the smallest root of a quartic polynomial.
    Marking note: Strong answers will mention the geometric construction and the Constitution. The mathematical detail is a bonus.
  5. What happened to the flag when Nepal became a republic in 2008?

    Nothing changed. Nepal kept the same flag. Some people argued for a new design, especially because of the flag's links to monarchy and Hinduism. The 2015 Constitution rejected these proposals and kept the 1962 design, including the same 24 geometric steps.
    Marking note: Award full marks for any answer that recognises that the flag stayed the same through the political change.
Discuss together

These questions have no single right answer. Talk in pairs or small groups, then share your ideas with the class.

  1. Most countries have a rectangular flag because European empires set that as the standard. Should countries that were never colonised be expected to follow this standard?

    This is a real question about cultural standards and global norms. Some students will say no — every country should be free to have its own design, including its own shape. Others will say yes — a global standard makes flags easier to recognise and respect, and Nepal is the odd one out. Both arguments have merit. The deeper point is that many 'global standards' are actually European inheritances. Rectangular flags are one example. Many other examples exist — calendars, time zones, business attire, alphabetical order. Nepal's flag is a reminder that the standards we take for granted were not made everywhere, and that some places have kept their own ways. End by asking: are there standards in your own country that came from somewhere else?
  2. When Nepal became a republic in 2008, some people argued the flag should change because it was tied to the monarchy. Other people said the flag belongs to the country, not to the government. Who was right?

    This is a real political debate that happened in Nepal. Some students will say the change-the-flag argument was right — symbols should match the system. Others will say the keep-the-flag argument was right — symbols should outlast governments. Both arguments are real. Strong answers will see that there is no easy right answer, and that different countries have made different choices. Russia changed its flag with the fall of the Soviet Union. The United States kept its flag through huge changes. South Africa changed its flag at the end of apartheid. Nepal kept its flag at the end of the monarchy. Each choice tells you something about how that country sees the relationship between government and country. End by asking: in your country, would you want the flag to change with the government?
  3. Nepal wrote the geometry of its flag into its Constitution. Is this a good idea, or should constitutions stick to laws and rights?

    This is a question about what should be in a constitution. Some students will say yes — making the flag precise is part of defining the country. Others will say no — constitutions should be about how the country is governed, not how its symbols are drawn. Both are valid. The deeper point is that constitutions are political documents that record what a country cares about. The fact that Nepal cared enough to put geometry in its Constitution shows that the flag was treated as a serious national matter, not a trivial decoration. Other countries put different things in their constitutions — some specify the national anthem, the national bird, the national flower, the national language. Nepal specified the national flag, down to the angles. End by asking: what would you put in your country's constitution if you were rewriting it?
Teaching sequence
  1. THE HOOK (5 min)
    Without saying anything about the lesson, ask: 'How many sides does a national flag have?' Most students will say four. Then say: 'Almost all of them do. There is exactly one exception in the world. Today we are going to find out about it.'
  2. INTRODUCE THE OBJECT (10 min)
    Show the flag of Nepal (sketch on the board if no image is available). Describe it: two stacked red triangles, with a blue border, with a white moon on top and a white sun below. Five corners. Taller than wide. Used by Nepal, a country in the Himalayas between India and China, with about 30 million people. Pause and ask: 'Why might Nepal have a different shape from every other country?' Listen to guesses. They will probably lead to the answer: Nepal was never colonised.
  3. THE HISTORY OF THE SHAPE (15 min)
    On the board, write: 'European empires set the global flag standard in the 1500s-1800s.' Explain: most countries adopted rectangular flags either during or after colonial rule. Nepal was never part of the British Empire, even though Britain ruled most of South Asia. So Nepal kept its older South Asian tradition of triangular pennants. The two triangles in the flag come from older flags used by different branches of the ruling dynasty. The exact modern flag was standardised in 1962. Discuss: this is a real case where 'being different' is a result of 'being free'.
  4. THE MATHEMATICS (10 min)
    Tell the students: the flag of Nepal is defined by 24 geometric construction steps in Schedule 1 of the Constitution. Anyone with a ruler and compass can follow them. The ratio of height to width is an irrational number. This is unusually precise. On the board, sketch the first few steps: 'Draw a line AB. From A, draw AC perpendicular to AB, making AC equal to AB plus one-third AB...' Discuss: why might a country put geometry in its Constitution? (To make the flag exact and unambiguous.)
  5. CLOSING (5 min)
    Ask: 'Nepal became a republic in 2008 but kept the same flag. Was that the right choice?' Take a few honest answers. End by saying: 'The flag of Nepal is more than a piece of cloth. It is a daily reminder that there are different ways to do things. The world has agreed on rectangular flags, but Nepal has not. That choice — to be different in this one small thing — is a quiet kind of freedom. Every Nepalese person who looks at their flag is reminded that they are not required to do things the way the rest of the world does. That is something worth thinking about.'
Classroom materials
Construct the Flag
Instructions: In pairs, students use rulers and compasses to draw a simplified version of the Nepalese flag, following the first few geometric steps. Step 1: draw a horizontal line AB. Step 2: from A, draw a perpendicular line AC equal to AB plus one-third AB. Step 3: from C, draw a line down to a point B that completes the bottom triangle. Continue as time allows. Each pair shares their drawing. Discuss: mathematics is a way of being exact.
Example: In Mr Sharma's class, students worked in pairs and most produced reasonable triangles. The teacher said: 'You have just done what every Nepalese flag-maker does. The Constitution gives you the instructions, and if you follow them carefully, you get the same flag every time. That is what mathematics is for in law: to be exact.'
Flags of the World
Instructions: On the board, list as many flag shapes as students can name. Most will be rectangles. A few will be squares (Switzerland, Vatican). The Ohio state flag is a swallowtail. Some military flags are triangles or other shapes. Discuss: how many shapes are possible? Why did the world end up with mostly one?
Example: In Mrs Khanal's class, students named maybe twenty flags before realising they were nearly all rectangles. The teacher said: 'You have just discovered what is normally invisible. The rectangle is so common that we stop seeing it. Nepal's flag makes us see it again. That is one of the reasons it matters — it makes the invisible visible.'
Design Your Own
Instructions: Each student designs a flag for themselves, their family, or their class. The flag does not have to be a rectangle. It should reflect something they care about. They can use any colours, any symbols, any shape. Display the flags. Discuss: what does each one say?
Example: In Mr Thapa's class, students designed flags in many shapes — circles, triangles, irregular polygons. One student designed a flag in the shape of an open book. Another designed a flag with the local mountain on it. The teacher said: 'You have just discovered that the rectangle is a choice. Most countries chose it. Some countries chose differently. You can choose what you like. The Nepalese flag is one example of what happens when a country chooses differently.'
Where to go next
  • Try a lesson on the wampum belt for another deeply symbolic object that records identity and history.
  • Try a lesson on the Logberg for another political object connected to the unique constitutional history of a nation.
  • Try a lesson on the Mongolian ger for another object from a country with deep roots in its land and a complex modern history.
  • Connect this lesson to history class with a longer project on the history of national flags. How did the rectangular flag become the global standard? Which countries have changed their flags, and why?
  • Connect this lesson to mathematics class with a longer project on geometric construction. The Nepalese flag is a real-world example of constructive geometry, the same kind taught in classical Greek mathematics.
  • Connect this lesson to citizenship class with a longer discussion of national symbols. What does it mean for a symbol to outlast a government? What does it mean for a country to keep its own ways even when the rest of the world has agreed on something else?
Key takeaways
  • The flag of Nepal is the only non-rectangular national flag in the world. It is also the only one that is taller than it is wide. It has five corners — two stacked triangles, sharing the same left edge.
  • The double-pennon shape comes from much older South Asian triangular flags used by rulers, temples, and military units for over a thousand years. Nepal kept this tradition because it was never colonised by a European power.
  • The exact modern flag was standardised in 1962, when civil engineer Shankar Nath Rimal designed it on the request of King Mahendra. The design includes 24 specific geometric steps in Schedule 1 of the Constitution.
  • The flag's symbolism includes the Himalayas, the bravery of the Nepalese people (the colour red), peace (the blue border), the eternal life of Nepal (the sun and moon), and the country's two main religions (Hinduism and Buddhism).
  • The flag survived major political change. When Nepal abolished the monarchy in 2008 and became a federal democratic republic, the new Constitution of 2015 kept exactly the same flag, with exactly the same 24 geometric steps.
  • The flag is a small daily reminder that the global standards we take for granted — like the rectangular flag — are themselves products of history, and that a country can keep its own ways even when the rest of the world has agreed on something else.
Sources
  • Flag of Nepal — Wikipedia (2026) [encyclopedia]
  • Constitution of Nepal — Government of Nepal (2015) [institution]
  • Nepali Flag Law and Construction Details — Flags of the World (FOTW) (2017) [institution]
  • Flag of Nepal: History, Meaning and Symbolism — World Country Flags (2025) [news]
  • Nepal: A Political History — John Whelpton (2005) [academic]