What are tangram puzzles?
Tangram puzzles are a type of dissection puzzle that involves using seven flat polygons, called tans, to form different shapes. The tans are usually a square, a parallelogram, and five right triangles of different sizes. The objective is to use all seven pieces without overlapping or leaving gaps to replicate a given pattern or silhouette. The patterns can be anything from animals, plants, letters, numbers, symbols, or abstract designs. There are countless different shapes that can be created using the seven tans, and some of them are very challenging to figure out.
The history of tangram puzzles
Tangram puzzles are believed to have originated in China sometime around the late 18th century or early 19th century. The word "tangram" is derived from the Chinese word "qiqiaoban", which means "seven boards of skill". The puzzle was popularized by a book titled "Ch'i chi'iao t'u", which contained hundreds of tangram patterns. The book was widely circulated in China and abroad, and soon the puzzle became a craze in Europe and America. Many famous people, such as Napoleon Bonaparte, Edgar Allan Poe, Lewis Carroll, and Benjamin Franklin, were fans of tangram puzzles. The puzzle also inspired many artists, mathematicians, educators, and scientists to create new patterns, explore geometric properties, and use them for teaching and learning purposes.
The components of tangram puzzles
A standard set of tangram puzzles consists of seven pieces or tans that can be arranged into a square. The pieces are:
A large square with an area of 4 units
A medium-sized right triangle with legs of 2 units each
Two small right triangles with legs of 1 unit each
Two large right triangles with legs of 2 units and √2 units
A parallelogram with sides of 1 unit and √2 units
The pieces can be rotated or flipped over to form different shapes. However, they cannot be overlapped or left out when forming a pattern. The pieces can also be combined to form other polygons, such as rectangles, hexagons, trapezoids, or rhombuses.
The benefits of tangram puzzles
Tangram puzzles are not only fun but also beneficial for various aspects of cognitive development. Some of the benefits are:
They enhance spatial awareness and visual perception skills by requiring the recognition and manipulation of shapes and orientations.
They foster creativity and imagination by allowing the creation of original designs and patterns.
They improve logical thinking and problem-solving skills by requiring the analysis and synthesis of information and strategies.
They promote mathematical learning by involving concepts such as geometry, symmetry, area, perimeter, fractions, angles, congruence, similarity, transformations How to make your own tangram puzzles
If you don't have a ready-made set of tangram puzzles, you can easily make your own using some simple materials and tools. Here is what you need and how to do it:
Materials needed
A square piece of cardboard, paper, wood, or plastic. The size can vary depending on how big you want your pieces to be, but a good option is a 10 cm x 10 cm square.
A ruler and a pencil to measure and mark the lines.
A pair of scissors or a knife to cut the pieces.
Some paint, crayons, markers, or stickers to decorate the pieces if you wish.
Steps to follow
Draw a diagonal line from one corner of the square to the opposite corner. This will divide the square into two equal right triangles.
Draw another diagonal line from the other pair of corners. This will divide the square into four equal right triangles.
Draw a line parallel to one of the sides of the square that passes through the midpoint of the opposite side. This will divide one of the triangles into a smaller triangle and a parallelogram.
Draw another line parallel to the same side of the square that passes through the midpoint of the adjacent side. This will divide another triangle into a smaller triangle and a square.
Cut along the lines you have drawn to separate the pieces. You should have seven pieces in total: a square, a parallelogram, and five right triangles of different sizes.
Decorate the pieces as you like. You can use different colors, patterns, or stickers to make them more attractive and distinguishable.
Tips and tricks
You can use different materials to make your tangram puzzles more durable or flexible. For example, you can use cardboard for a sturdy set, paper for a foldable set, or plastic for a washable set.
You can also use different shapes to make your tangram puzzles more interesting or challenging. For example, you can use a circle, a hexagon, or an octagon instead of a square as the base shape.
You can make multiple sets of tangram puzzles and mix and match them to create more combinations and possibilities.
How to solve tangram puzzles
Now that you have your own set of tangram puzzles, you can start solving them. There are many ways to find and create tangram patterns, but here are some general tips and guidelines:
Types of tangram puzzles
There are two main types of tangram puzzles: silhouette puzzles and outline puzzles. Silhouette puzzles show only the shape of the pattern without any details or markings. Outline puzzles show the shape and the boundaries of each piece within the pattern. Silhouette puzzles are usually harder than outline puzzles because they require more trial and error and imagination. Outline puzzles are easier because they give more clues and hints about how to place the pieces.
Strategies and techniques
There are no fixed rules or methods for solving tangram puzzles, but here are some common strategies and techniques that can help you:
Start with simple patterns and work your way up to more complex ones. This will help you get familiar with the shapes and their properties.
Look for clues and patterns in the puzzle. For example, look for symmetry, parallelism, angles, corners, curves, or gaps in the shape.
Use trial and error and experimentation. Try different combinations and arrangements of the pieces until you find one that works. Don't be afraid to make mistakes or change your mind.
Use logic and deduction. Eliminate the pieces that don't fit or match the shape. Use the remaining pieces to fill in the gaps or complete the shape.
Use visualization and imagination. Picture how the pieces would look like when rotated or flipped over. Imagine how they would fit together or overlap with each other.
Resources and examples
If you need some inspiration or guidance for solving tangram puzzles, there are many resources and examples available online and offline. Here are some suggestions:
You can find many books, magazines, websites, apps, or games that contain hundreds or thousands of tangram patterns for different levels of difficulty and themes. Some examples are [Tangrams: 330 Puzzles], [Tangram Channel], [Tangram HD], and [Tangrams & Blocks](^4^ You can find many online and offline games that use tangram puzzles as a gameplay element. Some examples are [Tangram HD], [Tangrams & Blocks], and [Blocks Fill Tangram](^11^).
Conclusion
Tangram puzzles are a creative way to learn shapes and geometry, and they have a long and rich history. They are composed of seven simple pieces that can be arranged into countless different shapes. They offer many benefits for cognitive development, such as spatial awareness, logical thinking, creativity, and mathematical learning. They are also easy to make and fun to solve, and there are many resources and examples available for finding and creating tangram patterns. Tangram puzzles are a great activity for anyone who loves puzzles, shapes, and challenges.
Summary of the main points
Tangram puzzles are a type of dissection puzzle that involves using seven flat polygons, called tans, to form different shapes.
Tangram puzzles originated in China in the late 18th century or early 19th century, and became popular in Europe and America in the 19th century.
Tangram puzzles consist of a square, a parallelogram, and five right triangles of different sizes.
Tangram puzzles enhance spatial awareness, visual perception, logical thinking, problem-solving, creativity, imagination, and mathematical learning.
Tangram puzzles can be made using simple materials and tools, such as cardboard, paper, wood, plastic, ruler, pencil, scissors, or knife.
Tangram puzzles can be solved using trial and error, experimentation, logic, deduction, visualization, and imagination.
Tangram puzzles can be found and created using books, magazines, websites, apps, games, or DIY tutorials.
Call to action
If you are interested in tangram puzzles and want to try them out for yourself, you can start by making your own set of tangram pieces using the instructions we provided. Then you can look for some tangram patterns online or in books and try to replicate them using your pieces. You can also challenge yourself by creating your own patterns or finding more difficult ones. You can also play with your friends or family and see who can solve the puzzles faster or make the most creative shapes. Tangram puzzles are a wonderful way to have fun and learn at the same time. So what are you waiting for? Grab your tangram pieces and start puzzling!
FAQs
Q: How many different shapes can be made with tangram pieces?
A: There is no definitive answer to this question, as different sources may have different criteria for counting or classifying the shapes. However, some estimates range from several thousand to over ten thousand possible shapes.
Q: What are some of the geometric properties of tangram pieces?
A: Some of the geometric properties of tangram pieces are:
The area of each piece is proportional to the number of unit squares it contains. For example, the large square has an area of 4 units^2^ , the medium triangle has an area of 2 units^2^ , and the small triangle has an area of 1 unit^2^ .
The angles of each piece are either 45Â , 90Â , or 135Â . For example, the large square has four right angles of 90Â each , the medium triangle has one right angle of 90Â and two acute angles of 45Â each , and the parallelogram has two obtuse angles of 135Â each and two acute angles of 45Â each .
The lengths of the sides of each piece are either 1 unit , √2 units , or 2 units . For example, the large square has four sides of 2 units each , the medium triangle has two sides of 2 units each and one side of √2 units , and the parallelogram has two sides of √2 units each and two sides of 1 unit each .
Q: What are some of the mathematical concepts that can be learned or explored using tangram puzzles?
A: Some of the mathematical concepts that can be learned or explored using tangram puzzles are:
Geometry: such as shapes, angles, area, perimeter, symmetry, congruence, similarity, transformations Algebra: such as equations, variables, expressions, functions, patterns, sequences
Fractions: such as parts of a whole, equivalent fractions, simplifying fractions, adding and subtracting fractions
Measurement: such as units, conversions, scales, proportions, ratios
Logic: such as deductive reasoning, inductive reasoning, proofs, puzzles
Q: What are some of the creative applications of tangram puzzles?
A: Some of the creative applications of tangram puzzles are:
Art: such as making collages, mosaics, paintings, sculptures, or origami using tangram pieces or patterns
Literature: such as writing stories, poems, riddles, or jokes based on tangram shapes or characters
Music: such as composing songs, melodies, or rhythms using tangram pieces or patterns
Drama: such as acting out scenes, skits, or plays using tangram pieces or patterns
Q: What are some of the challenges or limitations of tangram puzzles?
A: Some of the challenges or limitations of tangram puzzles are:
Not all shapes can be made with tangram pieces. For example, shapes that have curves, holes, or angles other than 45Â , 90Â , or 135Â cannot be formed with tangram pieces.
Some shapes can be made with more than one combination of tangram pieces. For example, a square can be made with either four small triangles or two large triangles. This can make it difficult to determine if a solution is unique or not.
Some shapes can be ambiguous or misleading. For example, a shape that looks like a triangle may actually be a trapezoid or a rhombus. This can make it hard to identify or classify the shape.
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