Just Some Guy

Please allow me to introduce myself, I'm a man of neither wealth nor fame.

I am not - repeat NOT - a mathematician. In fact, due to my lack of a good education (through no fault of my own) I have been so intimidated by and afraid of mathematics that I've avoided it like the plague for most of my life. But several years ago I read a few books about the history of mathematics, from the rope-stretchers of ancient Egypt to relatively modern times.

I grew enamored with many of the personalities involved in the development of the subject and the rivalries of people such as Newton and Leibnitz, the Bernouli clan, and others. And I found mathematics to be interesting and often quite beautiful.

So I purchased a good calculator (a TI-30XS MultiView) and developed the habit of playing with numbers the way children play with toys, not with any particular goal in mind, just as another form of entertainment.

Last year, while I was ensconced in a care facility recuperating from a heart attack I read all of the books they had that were of any interest to me and then quickly grew bored with the TV. So I got a friend to bring me a calculator so I could more easily play with numbers.

For a couple of weeks I found all of the prime numbers and the factors of composite numbers up to 5,000. That was about as far as I cared to go, for the time being, with that particular project, so next I turned my attention to Pascal's Triangle.

At the time I had no access to the internet, but I knew from previous reading that there are a lot of cool patterns within the Triangle, so I wanted to see how many I could remember. I remembered a few of them, then I decided to see if I could find any method of generating, directly, the sequences of numbers in the diagonals of the Triangle. I didn't really expect to succeed, but I thought it would be fun to give it a try. I knew how to build the Triangle row by row, using addition, but I wanted to see if I could build it diagonal by diagonal.

And it certainly was fun, especially when I actually succeeded!

That was about a year ago, and try as I might I can find nothing like it now that I have access to the internet. And then, just last week, I found a completely different method of doing the exact same thing!

So I'm here to hopefully get some feedback from real mathematicians concerning whether either of these methods are new, or if, perhaps, I've been scooped.

I'll make a post about this but I'm unsure where to put it. I guess "Basic Math" will do since, after all, it is pretty basic stuff.

 

Interesting, long story.

 

Thanks, I was beginning to think I wasn't going to get any response.

 

You've posted in the following thread?

https://www.math-forums.com/threads/the-diagonals-of-pascals-triangle.443492/

 

Yes, I was hoping to get some feedback.

 

Sound like you've come a long way in math. Good for you. I remember getting my first graphing calculator. I just used it all day seeing what every button did. Math is a great thing.

 

One of the things I like about math is how often pure math can become applied math.

 

Definitely. I have a friend how only likes pure math, and has no real interest in other math.

 

Number theory was generally regarded as fairly useless... until we needed really big prime products for computer security. Who knows what "pure" maths will next become application-critical?