Pythagorea 60°: A Unique Puzzle Game with Equilateral Triangles
Pythagorea 60: A Fun and Educational Game for Geometry Lovers
If you are looking for a game that can help you improve your geometry skills, challenge your logic and creativity, and entertain you at the same time, you might want to try Pythagorea 60. This game is a collection of more than 270 geometric problems that can be solved on a triangular grid without complex constructions or calculations. It is based on the principles of Euclidean geometry, the branch of mathematics that studies shapes, angles, distances, and proportions. In this article, we will tell you more about what Pythagorea 60 is, how to play it, why to play it, and where to download it.
What is Pythagorea 60?
Pythagorea 60 is a game that was developed by HORIS INTERNATIONAL LIMITED, a company that also created Euclidea, another popular game for geometry lovers. Pythagorea 60 is inspired by the ancient Greek mathematician Pythagoras, who is best known for his theorem about right triangles. The game is named after him because it often involves right angles and the Pythagorean theorem to compare lengths of segments and distances between points.
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A collection of geometric problems on a triangular grid
The game consists of more than 270 geometric problems of different kinds, such as finding the center of a circle, constructing an equilateral triangle, dividing an angle into three equal parts, or proving that two triangles are congruent. All these problems can be solved by using only straight lines and segments, and by setting points in line intersections. There are no sophisticated instruments or moves that are counted. The only thing that matters is the final result.
All the objects in the game are drawn on a grid whose cells are equilateral triangles. This means that all the angles in the grid are 60 degrees, hence the name of the game. The triangular grid adds a new dimension to the geometric problems, as it requires you to think differently from the usual square grid. You will have to use your spatial reasoning and imagination to find patterns, symmetries, and regularities in the shapes.
A way to learn and practice Euclidean geometry
Pythagorea 60 is not only a game, but also a learning tool. It covers most of the ideas and notions of elementary geometry, such as circles, angles, triangles, polygons, congruence, similarity, parallelism, perpendicularity, bisectors, medians, altitudes, circumcenters, incenters, orthocenters, centroids, etc. By playing Pythagorea 60, you will be able to understand important concepts and properties of Euclidean geometry, such as how to construct shapes using basic tools, how to use logic and deductive reasoning to prove statements, how to apply algebraic methods to solve geometric problems, etc.
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If you have just started your acquaintance with geometry, Pythagorea 60 will help you grasp the fundamentals and build a solid foundation. If you passed the course of geometry some time ago, Pythagorea 60 will help you refresh and check your knowledge and skills. If you are not on good terms with geometry, Pythagorea 60 will help you discover another side of the subject that is more fun and intuitive.
A challenge for your geometric intuition and creativity
Pythagorea 60 is not only a learning tool, but also a game. It offers a variety of problems that range from easy to hard, from simple to complex, from obvious to tricky. Some problems can be solved in a few seconds, while others may take you hours or even days to figure out. Some problems have one solution, while others have multiple or infinite solutions. Some problems are based on classic theorems or constructions, while others are original and inventive.
By playing Pythagorea 60, you will be able to test and improve your geometric intuition and creativity. You will have to find the best way to solve each problem, using the minimum number of moves and the maximum efficiency. You will have to look for hidden clues, alternative approaches, and unexpected connections. You will have to experiment, explore, and invent new methods and strategies. You will have to challenge yourself and have fun at the same time.
How to play Pythagorea 60?
Pythagorea 60 is easy to play, but hard to master. It has a simple and intuitive interface that allows you to draw lines and segments, move points, erase mistakes, and check solutions. It also has a clear and concise instruction that explains the goal and the conditions of each problem. Here are some basic tips on how to play Pythagorea 60.
The rules and the tools
The rules of Pythagorea 60 are simple: you have to solve each problem by using only straight lines and segments, and by setting points in line intersections. You cannot use curves, circles, arcs, angles, or measurements. You cannot move or delete existing objects. You cannot use any external tools or aids.
The tools of Pythagorea 60 are also simple: you have a triangular grid that serves as your paper, a point tool that allows you to set points on the grid or on existing lines, a line tool that allows you to draw lines through two points or extend existing segments, an erase tool that allows you to erase your own lines or points, a check tool that allows you to check if your solution is correct or not, and a reset tool that allows you to start over if you are stuck or unhappy with your solution.
The levels and the topics
The levels of Pythagorea 60 are organized into 15 topics that cover different aspects of Euclidean geometry. Each topic has a name and a symbol that represents its main idea or concept. For example, the first topic is called "Right Angle" and has a symbol of a right angle with two perpendicular lines. The second topic is called "Equilateral Triangle" and has a symbol of an equilateral triangle with three equal sides.
Each topic has 18 levels that increase in difficulty and complexity. The first level of each topic is usually an introduction or a tutorial that shows you how to solve a basic problem related to the topic. The last level of each topic is usually a challenge or a puzzle that requires you to apply all the skills and knowledge that you have learned in the previous levels.
The hints and the glossary
If you are having trouble with solving a problem, you can use the hint button that is located at the bottom right corner of the screen. The hint button will give you a clue or a suggestion on how to proceed with the problem. However, using the hint button will reduce your score for that level, so use it wisely and sparingly.
If you are not familiar with some terms or concepts that are used in the game, you can use the glossary button that is located at the top right corner of the screen. The glossary button will open a list of definitions and explanations for all the geometric terms and concepts that are used in the game. You can also access the glossary from the main menu by tapping on the question mark icon.
Why play Pythagorea 60?
Pythagorea 60 is more than just a game. It is also an educational and recreational activity that can benefit you in many ways. Here are some reasons why you should play Pythagorea 60.
To discover the beauty and naturalness of geometric constructions
Geometry is one of the oldest and most fundamental branches of mathematics. It deals with shapes, patterns, symmetries, proportions, and relationships that exist in nature and in human-made objects. Geometry is also one of the most beautiful and elegant branches of mathematics. It reveals hidden order, harmony, logic, and simplicity in complex phenomena.
By playing Pythagorea 60, you will be able to discover the beauty and naturalness of geometric constructions. You will be able to see how simple shapes and figures can be created by using only straight lines and segments, and by following some basic rules and principles. You will be able to appreciate the elegance and efficiency of geometric constructions, and how they can solve complex problems with minimal resources. You will be able to marvel at the beauty and diversity of geometric shapes, and how they can form intricate patterns an