Tangram

A tangram is a fun puzzle.

It uses seven flat shapes. You can use them to make pictures. You can follow a pattern in a book. You can also make your own art.

People first made these in China. They might have come from small tables. Some sets are made of wood. Other sets use glass or shell.

These puzzles became very popular in Europe. Many people liked playing with them. They are used for art and school today.

Can you make a new shape with the pieces?

A tangram is a special kind of puzzle. It uses seven flat shapes called tans.

You can use these pieces to make many shapes. Most people try to copy a pattern from a book. You must use all seven pieces. You cannot let the pieces overlap. You can also make your own art. People use tangrams for fun and for school.

These puzzles likely came from China. Some think they grew from small banquet tables. Long ago, people arranged these tables into pretty patterns.

Tangrams became a big trend in Europe. They were very popular in France and Denmark. In Germany, some sets were made of stone. Other sets were made of glass or even shell.

There are also math tricks called paradoxes. One trick uses two shapes that look the same. One shape has a foot, but the other does not. It looks like a piece is missing. But the shapes actually have the same area.

There are many ways to play. You can find over 6,500 different puzzles in old books. Even today, people make new ones.

A tangram is a fascinating dissection puzzle made of seven flat shapes. These pieces are called tans.

Most people play by trying to copy a specific pattern. You usually see an outline in a puzzle book. Your goal is to fill that outline using every single piece. You must not let any of the pieces overlap. Some people use the tans to create their own art. They make minimalist designs that look beautiful on their own.

There are specific rules for how the seven pieces work together. The set includes two large right triangles and one medium right triangle. You also get two small right triangles, one square, and one parallelogram. The parallelogram is a very special piece in the set. It is the only one without reflection symmetry. This means you might have to flip it over to make certain shapes. All seven pieces fit together perfectly to form one large square.

Many people believe the tangram was invented in China. It likely appeared around the late 18th century. Some think it grew from a tradition of small banquet tables. During the Song dynasty, a man named Huang Bosi used small tables for guests. He arranged six small tables into pretty patterns. Later, a seventh table might have been added to the set.

The puzzle traveled to the West on trading ships. An American captain named M. Donnaldson brought books about it to Philadelphia in 1816. Later, the puzzle became a huge craze in Europe. It was very fashionable in France and Denmark around 1818. In Germany, people sold sets called "The Anchor Puzzle" around 1891. These sets were sometimes made of stone or earthenware. The puzzle even saw a big comeback during World War I.

Tangrams can even create strange math tricks called paradoxes. These are known as dissection fallacies. One famous example is the "two-monks paradox" by Henry Dudeney. It shows two shapes that look almost identical. One shape has a foot, but the other one does not. It looks like a piece of area is missing. However, the second shape is actually slightly larger to make up for it.

A tangram is a type of dissection puzzle made of seven flat polygons. These individual pieces are known as tans.

The primary goal of the puzzle is to replicate a specific pattern. These patterns are often provided as simple outlines in puzzle books. To succeed, a player must use all seven pieces without any overlap. Some people use the tans for artistic purposes instead. They create minimalist designs that are valued for their aesthetic beauty.

To understand how a tangram works, one must look at its specific geometry. The seven pieces are designed to fit together to form a single large square. The set includes two large right triangles and one medium right triangle. There are also two small right triangles, one square, and one parallelogram. The parallelogram is a unique piece in the collection. It lacks reflection symmetry, meaning it only has rotational symmetry. Because of this, it is the only piece that may require flipping over to complete certain shapes.

Researchers have studied the many ways these pieces can be arranged. In 1942, Fu Traing Wang and Chuan-Chih Hsiung proved a specific mathematical limit. They showed there are only thirteen possible convex tangram configurations. A convex shape is one where any line drawn between two points stays inside the outline. While there are only thirteen convex shapes, the number of total possible patterns is massive. Over 6,500 different tangram problems were created from texts in the 19th century alone.

The exact origins of the tangram remain a subject of historical interest. It is widely believed to have been invented in China around the late 18th century. Some historians suggest the puzzle was inspired by the Song dynasty. During that era, a polymath named Huang Bosi used small banquet tables for entertainment. These six small tables, called feast tables or swallow tables, were arranged into patterns. It is possible a seventh table was added later to create the modern set.

As trading ships traveled, the puzzle moved from China to the West. In 1815, an American Captain named M. Donnaldson received books on the subject. He brought these books to Philadelphia in February 1816. This led to the first tangram books being published in America. The puzzle soon became a major craze in Europe. In Denmark, interest peaked around 1818 due to new publications. In Germany, an industrialist named Friedrich Adolf Richter marketed sets as "The Anchor Puzzle" around 1891. These sets were often made of stone or earthenware. The puzzle even saw a resurgence of popularity during World War I.

Tangrams are also used to demonstrate mathematical paradoxes, which are known as dissection fallacies. These occur when two shapes appear to be different sizes but use the same pieces. One famous example is the "two-monks paradox" attributed to Henry Dudeney. This paradox uses two similar shapes where one appears to be missing a foot. In reality, the area of the missing foot is compensated for by a slightly larger body. The change in area is hard to see because the math involves the square root of two.

Another interesting example is the "Magic Dice Cup" paradox found in Sam Loyd's work. This involves using the same seven shapes to create cups of different volumes. One cup might appear whole, while others contain different sized vacancies. These illusions show how the human eye can be tricked by geometric rearrangement.

Beyond simple play, the tangram connects to several broader fields. It is used in education to teach geometric reasoning and spatial skills. It also serves as a tool for art and minimalist design. The puzzle's history shows how a simple set of shapes can cross many cultures. It has moved from ancient banquet tables to modern classrooms and art galleries. This journey makes the tangram one of the most recognized dissection puzzles in the world.