Pythagoras’ theorem, named after the ancient Greek mathematician Pythagoras, states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The equation is also presented as A squared + B squared = C squared

Through the Pythagoras theorem equation, mathematicians can derive effective calculations in systems or projections. The following are some of the modern marvels that require the age-old equation!

Architects and engineers use Pythagoras’ theorem to ensure structural stability and accurate measurements in building design. It helps in determining the diagonal distances, ensuring that walls, floors, and roofs are perfectly aligned.

Specifically, the determining of squareness and right angles are effective in creating perpendicular walls, and square rooms. The theorem is also crucial to maintain structural stability. Architects calculate the lengths of diagonal bracings and cross supports, ensuring that structures can withstand forces and loads without collapsing.

Internally, it can be used to optimize space. By applying the theorem, architects can precisely measure the dimensions and proportions of rooms, hallways, and staircases, ensuring efficient use of available space and creating visually appealing designs. Further, the list of uses for Pythagoras goes on into landscaping, site planning, perspectives, and proportions.

Apart from its practical usage in building and physical structures, technological systems also require the use of Pythagoras theorem. Navigation systems, such as GPS (Global Positioning System). calculate distances between two points on a map or determine the shortest route between two locations, while optics and light-related calculations help to determine the focal length of lenses, calculate distances in optical systems, and understand the principles of reflection and refraction.

With the same concept of calculating distance, in computer graphics, Pythagoras’ theorem is used to calculate distances between points in a 2D or 3D space. It enables the creation of realistic visuals, simulations, and animations.

For example, game developers to calculate the distance between two points in a 2D or 3D space. By using the theorem’s formula (c² = a² + b²), the distance between two points (represented by the hypotenuse ‘c’) can be determined based on the differences in their coordinates (a and b along the x, y, and z axes). Other calculations include:

Collision detection: Pythagoras’ theorem is utilized in collision detection algorithms. When determining if two objects in a game world collide, their positions and dimensions are compared. By calculating the distance between the objects’ centers using the theorem, developers can determine if they intersect or are within a certain collision radius.

Camera movement and perspective: In computer graphics, Pythagoras’ theorem helps determine the position and movement of virtual cameras. By applying trigonometry and Pythagoras’ theorem, developers can calculate the camera’s position, rotation, and field of view to create various perspectives and viewpoints within the game world.

Pathfinding and AI navigation: In games with AI-controlled characters or NPCs, Pythagoras’ theorem is used in pathfinding algorithms. By calculating the distance between different points on a map or grid, developers can determine the most efficient route for characters to move, avoiding obstacles and reaching their destinations.

Lighting and shading: In computer graphics, Pythagoras’ theorem is employed to calculate the intensity of light and shadows. By determining the distance between a light source and a surface point, developers can calculate the light’s attenuation (decrease in intensity with distance) and simulate realistic lighting effects.

Overall, Pythagoras’ theorem plays a fundamental role in game development and computer graphics by providing the mathematical foundation for distance calculations, collision detection, camera movement, pathfinding, and lighting effects.

With a glimpse of Pythagoras theorem and the various fields that it can be used in, get started in learning secondary school maths with Musclemath. At Musclemath, our teachers will be willing to share knowledge and go the extra mile. Though these lessons do not cover the above content on how Pythagoras theorem is used, having an interest in the subject is crucial to fuel your journey of knowledge, explore more here.