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Tetris board.Image credit: Brandnard/Wikimedia Commons
With its bright colors, easy-to-learn rules and familiar music, the Tetris video game has been a pop culture icon for the past 40 years. Many people, like me, have been playing the game for decades, and it has evolved to accommodate new technologies like gaming systems, phones, and tablets. But until January 2024, no one has been able to beat it.
A teenager from Oklahoma has become the Tetris champion after crashing and beating level 157. Beating it means the player moves pieces too fast and the game can’t keep up with the score, causing the game to crash. Artificial intelligence can come up with strategies that allow players to control game tiles more effectively and place them into place faster—strategies that helped lead to the game’s first winner.
But there’s more to Tetris than the elusive promise of victory. As a mathematician and mathematics educator, I recognize that this game is based on a fundamental element of geometry called dynamic spatial reasoning. Players use these geometric skills to manipulate game pieces, and playing the game both tests and improves players’ dynamic spatial reasoning abilities.
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Russian computer scientist Alexey Pajitnov invented Tetris in 1984. The game itself is very simple: the Tetris screen consists of a rectangular game board with falling geometric figures. The figures are called tetrominoes and are made up of four squares connected in seven different configurations.
Game pieces fall from the top, one at a time, and stack from the bottom. Players can manipulate each falling object by turning or sliding it before dropping it to the bottom. When a row is completely filled, it disappears and the player receives points.
As the game progresses, pieces will appear at the top faster, and the game ends when the pile of pieces reaches the top of the board.
dynamic spatial reasoning
Manipulating game parts exercises players’ dynamic spatial reasoning skills. Spatial reasoning is the ability to visualize geometric shapes and how they move in space. Dynamic spatial reasoning is therefore the ability to visualize actively moving figures.
Tetris players must quickly decide where the currently dropped game tile best fits and then move it there. This motion involves translation (that is, moving the shape left and right) and rotation (that is, rotating the shape on its axis in 90-degree increments).
Spatial visualization is partly an innate ability, but partly a learned expertise. Spatial skills are considered by some researchers to be necessary for successful problem solving and are often used along with mathematical skills and language skills.
Spatial visualization is a key component of a mathematical subject called transformation geometry, often first taught in secondary schools. In a typical transformation geometry exercise, students might be asked to represent a figure in terms of its x and y coordinates on a coordinate graph and then identify the transformations required to move it from one position to another, such as translation and rotation, Also leave that part unchanged. Same shape and size.
Reflection and dilation are two other basic mathematical transformations, although they are not used in Tetris. Reflection flips the image onto either line while maintaining the same size and shape, while dilation changes the size of the shape, resulting in a similar figure.
For many students, these exercises are tedious because they involve plotting many points on the graph to move the position of the graph. But games like Tetris can help students master these concepts in a dynamic and engaging way.
Transform Geometry Beyond Tetris
Although transformation geometry may seem simple, it is the basis for several advanced topics in mathematics. Architects and engineers alike use transformations to create blueprints, representing the real world as scale drawings.
Animators and computer graphic designers also use the concept of transformations. Animation involves representing the coordinates of a shape in a matrix array and then creating a sequence to change its position, thereby moving it on the screen. While today’s animators use computer programs to automatically move characters, they are all translation-based.
Calculus and differential geometry also use transformations. The concept of optimization involves representing a situation as a function and then finding the maximum or minimum value of that function. Optimization problems typically involve graphical representations, where students use transformations to manipulate one or more variables.
Many real-world applications use optimization – for example, a business may want to find the lowest cost of distributing a product. Another example is working out the dimensions of a theoretical box with the largest possible volume.
All these premium themes use the same concepts as the simple moves of Tetris.
Tetris is an engaging and fun video game that players with morphing geometry skills may find success playing. Research has found that manipulating rotation and translation in games can provide a solid conceptual foundation for advanced mathematics in many areas of science.
Playing Tetris might lead students to future competencies in business analysis, engineering, or computer science, and it’s fun. As a math educator, I encourage my students and friends to keep playing.
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