Euclidean simplex
Dear little one,
Imagine you have a bunch of points in a three-dimensional space. Now, imagine that you connect some of these points to each other to form a shape, and that shape has only flat surfaces and straight edges, like a triangle. That's called a simplex.
A euclidean simplex, in particular, is a type of simplex where it has a very specific number of vertices or points, depending on the dimension of the space it lives in. For example, a 2D euclidean simplex (or a triangle) will always have three vertices or points, and a 3D euclidean simplex (or a tetrahedron) will always have four vertices or points.
But why is it called "euclidean"? That's because it follows the geometry of regular euclidean space, where parallel lines never meet and the angles of a triangle always add up to 180 degrees. This means that the euclidean simplex behaves consistently and predictably in this kind of space.
So, imagine you have a 3D euclidean simplex, a tetrahedron, with four points that connect to each other forming four triangles. You could move or rotate this shape, but it will always have the same number and arrangement of points, edges, and surfaces. And, because it's a mathematical object, it has some awesome properties and behaviours that can be studied and used in different fields.
Now, wasn't that simple, little one?
Imagine you have a bunch of points in a three-dimensional space. Now, imagine that you connect some of these points to each other to form a shape, and that shape has only flat surfaces and straight edges, like a triangle. That's called a simplex.
A euclidean simplex, in particular, is a type of simplex where it has a very specific number of vertices or points, depending on the dimension of the space it lives in. For example, a 2D euclidean simplex (or a triangle) will always have three vertices or points, and a 3D euclidean simplex (or a tetrahedron) will always have four vertices or points.
But why is it called "euclidean"? That's because it follows the geometry of regular euclidean space, where parallel lines never meet and the angles of a triangle always add up to 180 degrees. This means that the euclidean simplex behaves consistently and predictably in this kind of space.
So, imagine you have a 3D euclidean simplex, a tetrahedron, with four points that connect to each other forming four triangles. You could move or rotate this shape, but it will always have the same number and arrangement of points, edges, and surfaces. And, because it's a mathematical object, it has some awesome properties and behaviours that can be studied and used in different fields.
Now, wasn't that simple, little one?
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