Ptolemy's inequality
Ok kiddo, do you know what numbers are bigger or smaller than other numbers?
Great! Now imagine you have three different numbers, let's call them A, B, and C. Ptolemy's inequality says that:
AB + AC ≤ BC + A⁄C×B
Basically, it is a way to compare how big or small the sides of a special kind of shape called a quadrilateral are. Think of a quadrilateral as a shape with four sides, kind of like a square or a rectangle.
Now, if we use Ptolemy's inequality, we can compare the lengths of the sides of a quadrilateral to see if it's a special kind of quadrilateral called a cyclic quadrilateral. That means if you draw a circle around it, all four points of the quadrilateral will touch the circle.
So, Ptolemy's inequality helps us figure out if a quadrilateral can be a cyclic quadrilateral based on the lengths of its sides. Pretty cool, right?
Great! Now imagine you have three different numbers, let's call them A, B, and C. Ptolemy's inequality says that:
AB + AC ≤ BC + A⁄C×B
Basically, it is a way to compare how big or small the sides of a special kind of shape called a quadrilateral are. Think of a quadrilateral as a shape with four sides, kind of like a square or a rectangle.
Now, if we use Ptolemy's inequality, we can compare the lengths of the sides of a quadrilateral to see if it's a special kind of quadrilateral called a cyclic quadrilateral. That means if you draw a circle around it, all four points of the quadrilateral will touch the circle.
So, Ptolemy's inequality helps us figure out if a quadrilateral can be a cyclic quadrilateral based on the lengths of its sides. Pretty cool, right?
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