I really think Euler himself would be pleased with this result. I might have to get Geometer's sketchpad and check for myself, but do you think the Omega Triangle of the first Omega Triangle is the original triangle, or yet another triangle? In which case I wonder if you ever do get back to the original by taking successive Omega Triangles?
@benthurston27 It looks plausible that the blue orthocenter of the Omega Triangle is A2. And if I'm doing it right I think A1 might be the red orthocenter of the Omega Triangle and A3 the green but a couple times it only looked to me like the colored orthocenters from two of the vertices intersected at a point and not all 3 but I know they are all three supposed to meet at the same point, so I don't know.
@benthurston27 You can also get free software that does more or less the same things as Sketchpad, namely C.a.R. (by Rene Grossman) and Geogebra.
As for iterating the Omega triangle, that is an obviously interesting idea, and I have experimented somewhat with that, but could not find any periodicity.
I really think Euler himself would be pleased with this result. I might have to get Geometer's sketchpad and check for myself, but do you think the Omega Triangle of the first Omega Triangle is the original triangle, or yet another triangle? In which case I wonder if you ever do get back to the original by taking successive Omega Triangles?
benthurston27 6 months ago
@benthurston27 It looks plausible that the blue orthocenter of the Omega Triangle is A2. And if I'm doing it right I think A1 might be the red orthocenter of the Omega Triangle and A3 the green but a couple times it only looked to me like the colored orthocenters from two of the vertices intersected at a point and not all 3 but I know they are all three supposed to meet at the same point, so I don't know.
benthurston27 6 months ago
@benthurston27 You can also get free software that does more or less the same things as Sketchpad, namely C.a.R. (by Rene Grossman) and Geogebra.
As for iterating the Omega triangle, that is an obviously interesting idea, and I have experimented somewhat with that, but could not find any periodicity.
njwildberger 6 months ago
lol nice drum stick but very helpfull as i am curently doing an assignment at school
thankyou
ilovehb94 1 year ago
I presume you are familiar with Sir William Rowan Hamilton's articles on anharmonics.
RSKueffner 2 years ago
No I am not. Please explain what it is roughly and why it might be relevant, thanks.
njwildberger 2 years ago