by Ysh » Mon Jan 23, 2017 8:07 pm In celebrate of my 4000th postings, I have create great thread of decagonal number. Of which of course 4000 is this type of number! For those who maybe do not know, decagonal number is a type of figurate number for decagon polygon (10 sider polygons). And for those who still do not know of this figurate number, I can do explainings:
Back in many moons ago some mathematics men work with the stone pebble for looking at number. They think that number makes up some of all the world. And that all the world can be understood through number. What is best way to relate physical shape with number? To make physical shape out of number. It is very simple concepts. So you can have some shape like as example triangle and make it out of same number of pebbles on each side. Then you can have some triangle as subset of this overall triangle, using one less pebble on each side. You can see here:
In first frame, it is just one pebble per side, which is just one pebble. Next it is 2 pebble per side, which makes 3 total pebble. Next is 3 pebble per side, which make for 6 total pebble. You can see here that once we go up to 6 it is easy to see this subset property. Inside of this 3 pebble sided triangle is a 2 pebble sided triangle, so we can draw lines here to indicate this one. Next is 10 total pebbles for 4 pebble sided triangles. You can see that we must add this extra pebble to the inside to make the 3 pebble sided subtriangle. And finally we have 15 total pebble from 5 pebble sided triangle. So first 5 triangular numbers is 1, 3, 6, 10, and 15. So you can see here that you can not make a set of triangles in this way with 13 pebbles as example, since 13 is no triangular number!
It is same notions with this decagonal number except with decagon instead of triangle. So this one would look like this:
So as I say in beginning, this 4000 is decagonal number. A so-called very interest number! I will like to show it, but I can not find image of this large diagram.
But I think you all in Haven and Hearth community is intelligent men and can using some imagination to vision it within eye of minds. Is there some other numeric property my friends here can find interesting? Is your postings score a very interest number? I am very interest to hear of these interests! Thanks to you as always for your consideration!
