One way is to look on math.stackexchange.com and elsewhere online to see if anything is already known about whatever you've found. If not, *politely* ask there; stating your discovery as a question: "Is this correct, and if so is it already known? I found this interesting, but have no idea whether it's of any importance to anyone else."
Try to set yourself apart from cranks trying to trisect angles, square the circle, etc., if you want to be taken seriously.
PS: I'd avoid asking at MathOverflow (another StackExchange math site, but oriented toward professionals), unless you well-grounded in the full standard curriculum and have done your own investigations into what is already known about your particular discovery. You could add that to the places you search before asking though:
Looking back at your previous question which didn't get any answers, IMHO it is unlikely this is a new discovery of any worth (sorry!). Any area of mathematics that is essentially easy will have picked to pieces by people over the years and all the good stuff has gone.
There are all sorts of patterns embedded into things like Pascal's Triangle. The most common and useful will be taught to students, such as the rows being the binomial coefficients, but there are plenty of patterns you can spot that are kind of interesting but which don't really lead anywhere new or useful. These things are great fun to discover for yourself but probably not the sort of thing that gets published.
Talk to a mathematician in your local university, he will tell you what your idea is worth, and whether it's new or not.
He can also sponsor you to get allowed to publish the proof on ArXiv. You don't really care about being published in rank-A peer-reviewed magazines since you don't have the "publish or perish" pressure: ArXiv is what give the largest visibility amongst researchers, peer-reviewed articles are mostly to build a CV or to attract funding.
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One way is to look on math.stackexchange.com and elsewhere online to see if anything is already known about whatever you've found. If not, *politely* ask there; stating your discovery as a question: "Is this correct, and if so is it already known? I found this interesting, but have no idea whether it's of any importance to anyone else."
Try to set yourself apart from cranks trying to trisect angles, square the circle, etc., if you want to be taken seriously.
https://math.stackexchange.com/
PS: I'd avoid asking at MathOverflow (another StackExchange math site, but oriented toward professionals), unless you well-grounded in the full standard curriculum and have done your own investigations into what is already known about your particular discovery. You could add that to the places you search before asking though:
https://mathoverflow.net/
Looking back at your previous question which didn't get any answers, IMHO it is unlikely this is a new discovery of any worth (sorry!). Any area of mathematics that is essentially easy will have picked to pieces by people over the years and all the good stuff has gone.
There are all sorts of patterns embedded into things like Pascal's Triangle. The most common and useful will be taught to students, such as the rows being the binomial coefficients, but there are plenty of patterns you can spot that are kind of interesting but which don't really lead anywhere new or useful. These things are great fun to discover for yourself but probably not the sort of thing that gets published.
Talk to a mathematician in your local university, he will tell you what your idea is worth, and whether it's new or not.
He can also sponsor you to get allowed to publish the proof on ArXiv. You don't really care about being published in rank-A peer-reviewed magazines since you don't have the "publish or perish" pressure: ArXiv is what give the largest visibility amongst researchers, peer-reviewed articles are mostly to build a CV or to attract funding.
First get it 'peer-reviewed' before publishing!