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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
Get started now by creating a new collection.
I went down the same rabbit hole and I can tell you that optimizing calculations won't help you here. You have to find a sublinear method based on the triangle's properties.
Too late to change the requirements...