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Apollonius - the architect behind the scenes
Proving theorems or identities is a skill. What I like about it is how it reuses familiar concepts. In this case, the Cosine Law and angle identities. With this, we can uncover something new. Apollonius is telling us that there is something about the relationship between the sides of a triangle and its median.
Does it have a practical application? Though this theorem may not headline a NASA mission or surgical procedures in hospitals, its geometric DNA is everywhere -- from the way we model forces in engineering to how we reconstruct the human body in 3D scans.
It is a quiet contributor to how math moves the world.
Have fun learning
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