The Seven Shapes of Creativity: A Guide to Tangrams
Tangrams are a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form specific shapes. This guide explores the history and logic of tangrams, offering strategies to improve your spatial reasoning and problem-solving skills.
The tangram is an ancient and elegant dissection puzzle. It consists of seven flat geometric shapes, called "tans," which are cut from a single square. The objective is to arrange all seven pieces, without overlapping, to form a specific shape, which is usually given only as a silhouette. Tangrams are a powerful tool for developing spatial reasoning, geometric intuition, and creative problem-solving. This guide will explore the logic of the seven tans and provide you with strategies to master this timeless puzzle.
Meet the Seven Tans
The magic of the tangram comes from the specific relationships between its seven pieces. All are derived from a single square. The set consists of:
- Two large right triangles
- One medium right triangle
- Two small right triangles
- One square
- One parallelogram
Understanding the relative sizes and angles of these pieces is fundamental. For instance, the two small triangles can form the medium triangle or the square. The medium triangle and the square can be formed by the two small triangles. All angles are multiples of 45 degrees (45°, 90°, 135°).
Strategies for Solving Tangram Puzzles
Solving a tangram is a process of visual trial and error, but it can be guided by logic.
1. Start with the "Bookends": The Large Triangles
The two large triangles are the biggest pieces and take up half the total area of the original square. They are often the easiest to place. Look for long, straight edges or right-angled corners in the silhouette that could only be formed by these large pieces. Placing them first provides a strong anchor and significantly reduces the remaining area you need to fill.
2. Identify Key Features
Look for distinctive features in the silhouette that hint at specific pieces:
- A square corner: This could be the square piece itself, or two triangles put together.
- A "pointy" corner (45 degrees): This must be one of the triangles.
- A parallelogram-shaped section: The parallelogram is a unique piece. It has no right angles. If you see a slanted, four-sided section, it's very likely the parallelogram. Remember that the parallelogram can be flipped over to slant the other way.
3. Think in Terms of Area and Negative Space
As you place pieces, pay attention to the shape of the empty space (the "negative space") you are creating. Does the empty area look like one of the remaining pieces? Sometimes, focusing on the shape of the hole is more helpful than focusing on the piece you are trying to place.
4. Don't Be Afraid to Start Over
It's very common to get partway through a solution only to find that the last few pieces won't fit. This is not a failure; it's part of the process. It simply means one of your earlier placements was incorrect. Don't be afraid to take pieces off the board and try a different arrangement. Every attempt gives you more information about what doesn't work, which is just as valuable as knowing what does.
The Benefits of Tangrams
Tangrams are more than just a game. They build crucial cognitive skills, including spatial visualization, problem-solving, and understanding of geometric concepts like symmetry, congruence, and area. They encourage patience and persistence. For children, they are a playful introduction to geometry. For adults, they are a meditative exercise in logic and creativity. By working with these seven simple shapes, you are engaging in a timeless practice of seeing the whole in the parts and the parts in the whole.