Of late, the New York times has been making headlines (which is of course their prerogative) out of ranking things.
The 100 books of the century.
The 100 movies of the century.
The 25 best pizzas in NYC (inexplicably updated six months later to “The 22 best pizzas in NYC,” portending a grim future where the category of “best pizza places” contracts toward some kind of pizza singularity).
Anyway, I say anyone can play at this game, and I hereby give you…
(And I’m sorry for the snub, 30-60-90-stans.)
EDIT: For future reference, a few other nominations from folks on social media…
- The 13-14-15, whose integer altitude of 12 divides the 14 into 5 and 9 (via Jutta Gut and David Williams)
- The 20-21-29, the smallest Pythagorean triple where c > b + 2 (via Dylan Rambow)
- The 80-80-20, which gives rise to the fabulous constructions of Langley’s Adventitious Angles (via Ng Boong Leong)
- The 3-5-7, which has a 120 degree angle, and can thus be attached to the 5-5-5 equilateral to create a 5-7-8 (via David Williams)
- The 1-i-0 (via lowcheeliang)
The 1-i-0 should take the ith spot in the list!
It does, we just can’t see it because the ith spot is directly orthogonal to the real-numbered list
Shouldn’t that be 1-i^2-0?
Sorry to nitpick…
But you forgot the Citgo triangle!
I believe that the standard fundamental domain of the modular group, with two vertices on the unit circle and one out at infinity (https://en.wikipedia.org/wiki/Fundamental_domain) is destined to be THE triangle of the 21st century. And that’s no mere hyperbole.
@Ben Orlin
Thank you, 🙏🏻 Ben, for sharing your list of the best triangles. 📐 Mathematics is a realm of the unimaginable, filled with things we can’t see and concepts that are yet unknown. 🌌 It brings these ideas to life through equations. For me, everything about mathematics is remarkable. ✨ It is a vast canvas where curious minds can paint a picture 🎨 and play with numbers while allowing their imagination to run wild—much like how you showcased the ten best triangles.
[I employ Grammarly AI for writing]
I’m partial to the ol 11-60-61
Fun and creative question! Since you said “triangles of the 21st century”, I’ll assume you mean famous smash karts or iconic “triangles” in a broad, cultural sense — not just geometry, but symbolic triangles in film, sports, design, relationships, music, and technology.
Math contestants will know the 4-5-6 triangle well – it is the only triangle with integer sidelengths and one angle is twice the other. Oh, and it’s also smallest acute scalene triangle with integer sidelengths.
Niche, I know, but still nice
I vote for the 36-72-72 triangle.
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