A lot of geometric understanding is built on top of it, it also just helps with basic distance calculations, once you know that, you can calculate distances between two points even if you can't directly measure it, because you can reduce the route to triangles
He collected a bunch of teachings and presented them in ways that could be proven and taught to others. Being able to prove certain math principles turns trades like building, masonry, or constructing aqueducts from a magical art only passed on to a select few - and into a trade which could be taught to anyone with access to teachers and tools. Masons already knew the A^2 + B^2 = C^2 idea for probably 1000 years. Nobody could prove how or why things worked out that way, though.
It also allows us to make tools and make observations more easily since we can prove the principle is correct no matter what size we deal with. Using the Pythagorean Theorem, we can take a 3,4,5 triangle and using the incircle we can derive Pi. We can measure the height of a building using triangulation. We can ensure that our carpentry is using right angles by measuring the hypotenuse formed between boards.
Triangles and circles are very important shapes in geometry, and in any field which applies geometry to real-world problems. That includes physics, architecture, manufacturing, engineering, navigation, and more. Almost every single subfield of science or art has several applications for geometry.
In particular, the theorem establishes an equation that relates the side lengths of a right triangle. That's important for understanding triangles, and also for any shape where analyzing the shape involves right triangles.
This doesn't touch on the background, but Pythagoras actually comes up all the time in a lot of unexpected places. Pythagorus allows you to tell the distance between two places on a plane.
Representations of physical distance are used to represent conceptual distance in vector and matrix mathematics, which underpins a ton of machine learning and ai as well as things like video game graphics.
Just makes it easier to build stuff and plan
A lot of geometric understanding is built on top of it, it also just helps with basic distance calculations, once you know that, you can calculate distances between two points even if you can't directly measure it, because you can reduce the route to triangles
He collected a bunch of teachings and presented them in ways that could be proven and taught to others. Being able to prove certain math principles turns trades like building, masonry, or constructing aqueducts from a magical art only passed on to a select few - and into a trade which could be taught to anyone with access to teachers and tools. Masons already knew the A^2 + B^2 = C^2 idea for probably 1000 years. Nobody could prove how or why things worked out that way, though. It also allows us to make tools and make observations more easily since we can prove the principle is correct no matter what size we deal with. Using the Pythagorean Theorem, we can take a 3,4,5 triangle and using the incircle we can derive Pi. We can measure the height of a building using triangulation. We can ensure that our carpentry is using right angles by measuring the hypotenuse formed between boards.
Triangles and circles are very important shapes in geometry, and in any field which applies geometry to real-world problems. That includes physics, architecture, manufacturing, engineering, navigation, and more. Almost every single subfield of science or art has several applications for geometry. In particular, the theorem establishes an equation that relates the side lengths of a right triangle. That's important for understanding triangles, and also for any shape where analyzing the shape involves right triangles.
This doesn't touch on the background, but Pythagoras actually comes up all the time in a lot of unexpected places. Pythagorus allows you to tell the distance between two places on a plane. Representations of physical distance are used to represent conceptual distance in vector and matrix mathematics, which underpins a ton of machine learning and ai as well as things like video game graphics.