Math thing I learned in using rational geometry instead of trigonometry:
Find the area of a triangle whose corners are at (1,1), (4,6), (8,3)
You can use Heron's formula, which would be really messy and have all sorts of square roots that you need to get. You can be way more clever and get the enclosing rectangle and subtract the three right triangle areas. But fundamentally, these areas are rational. You don't need heavy machinery of trigonometry to solve them and there are some really nice formulas you can derive that make problems like this trivial and less prone to using calculus-derived, complicated functions over irrational or transcendental numbers.
jimmysong /
npub10v…psp42
2025-06-02 20:01:41
Author Public Key
npub10vlhsqm4qar0g42p8g3plqyktmktd8hnprew45w638xzezgja95qapsp42Published at
2025-06-02 20:01:41Event JSON
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"content": "Math thing I learned in using rational geometry instead of trigonometry:\n\nFind the area of a triangle whose corners are at (1,1), (4,6), (8,3)\n\nYou can use Heron's formula, which would be really messy and have all sorts of square roots that you need to get. You can be way more clever and get the enclosing rectangle and subtract the three right triangle areas. But fundamentally, these areas are rational. You don't need heavy machinery of trigonometry to solve them and there are some really nice formulas you can derive that make problems like this trivial and less prone to using calculus-derived, complicated functions over irrational or transcendental numbers.",
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