Before I know something about the geometry, the mathematics equals algebra. Algebra is really an art of abstract while the geometry will bring you back to real life. In other word, maths doesn’t always mean an accurate calculation with each steps clearly. Don’t panic, I mean sometimes we will get the answer just like a magic. The nomogragh is a typically skill to get an answer of equations without analytic solution.
The first time I heard that the equation could have no analytic solution I think it unbelievable, but you know that the answers is always coming with the problem which you may heard the first time. In fact, sometimes the problems will not be noticed until someone find answers of them. For example, before Jobs told you the effect of retina display, you may never find you screen grainy. So we could get the answers of almost any equation by so many approximation skills. When we talk about the computer, most of the time we are using the their ability of approximation, in other words, the core of the computer is their algorithms which could be coded. As far as I can see, the algorithms could be coded but not be created by the computer itself so if some algorithms were hard to coded, the computer can only get the answer from iteration. But we all know the technology of word recognize and we only need few points to find a word by machine learning. So what if solve a equation by the same idea, I mean we needn’t every step return a certain number and we just use some geometry skills. Yes, the answer is nomograph.
If you could get the idea of how to find the questions, all you should do is just Google the keywords. I mean, the nomograph is a simple way to give out an answer to a complex equation while all you need to do is just draw some lines and find the numbers on the scales. If this idea could be contained in some algorithms of machine learning, we may get an increase of calculation speed. I mean the base layer of some algorithms could be a solution from nomograph. I don’t know whether or not this algorithms show a better performance, it is just an idea when I found the geometry could be used to solve some complex equations.