Talk:Gnomon (figure)

Figure wanted

As a not-very-mathematical (nor very visual) user, I had a time understanding the relationship between the gnomon and the parallelogram. Does anyone have a figure or illustration? Thanks --Ben 11:43, 19 April 2007 (UTC)

Image added. ~ Oni Lukos _ct 23:46, 21 July 2007 (UTC)

factoring property

Has anyone else noticed that our (recursively) thus far known gnomon (n^2), increased by one "segment" (+2n+1), factors to ((n+1)^2)? Therefore, (n+1)^2=(n+1)(n+1)=1n^2+2n+1. This works for any other exponent too:

(n+1)^3=(n+1)(n+1)(n+1)=1n^3+3n^2+3n+1

(n+1)^4=(n+1)(n+1)(n+1)(n+1)=1n^4+4n^3+6n^2+4n+1

(n+1)^5=(n+1)(n+1)(n+1)(n+1)(n+1)=1n^5+5n^4+10n^3+10n^2+5n+1

(n+1)^6=(n+1)(n+1)(n+1)(n+1)(n+1)(n+1)=1n^6+6n^5+15n^4+20n^3+15n^2+6n+1...

Also, if you examine the coefficients of the expanded forms(Bold), they digitally add to the respective exponent of eleven(Italic)(above):

11^2=121

11^3=1331

11^4=14641

11^5=161051

11^6=1771561 —Preceding comment added by varka (talk) 05:31, 7 March 2008 (UTC)

See Pascal's triangle --Oni Lukos _ct 06:13, 7 March 2008 (UTC)

Questions

The definition and picture seem to suggest gnomon as nonconvex hexagonal plane region. The application to polygonal numbers would think of it as a line of dots with one bend. For p-polygonal numbers would one not need p-2 bends? After all, polygonal numbers need not be composite. Is there a name for the region obtained by removing a small polygon from a larger similar one with which it shares a corner?--Gentlemath (talk) 00:45, 16 February 2009 (UTC)

Too narrow definition

The definition "In geometry, a gnomon is a plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram" seems too narrow. See: here, here, and here. JocK (talk) 01:43, 25 March 2009 (UTC)

Quite right. But see the main article gnomon. I would hate to see this diagram in that article but without the diagram this could just fold into that page. --Gentlemath (talk) 02:21, 25 March 2009 (UTC)

The generic geometric definition is hidden in the article gnomon. I have added a sentence to the definition here, as this seems the appropriate place for a proper geometrical definition. A merger into the article gnomon would perhaps be preferrable. JocK (talk) 01:26, 26 March 2009 (UTC)

bad definition

I was reading up on this in my old New Book of Knowledge Encyclopedia Series, and it give it a MUCH better, more insightful definition than what is given here. the section I will quote from appears to be written by Patricia G Lauber,

"Gnomon Numbers and Square Numbers:

You can also arrange objects in an "L" shape. This shape is Called Gnomon. The vertical part of the L has as many objects in it as the horizontal part. You can arrange any odd number of objects in the shape of a Gnomon."

(the book then diagrams the gnomons of 3, 5, and 7 simply using zeros as the objects. These Gnomons have the L shape and the median object is the corner of the L.)

"Another shape the Greeks studied was the square. A number is square if objects representing the number can be arranged in the shape of the square. to be a square, the figure must have the same number of rows as it has columns. The number 9 can be represented by a square. The square has 3 rows and 3 columns. you can add up the rows or columns and get 9. This is the same thing as writing 3x3. You have "squared" 3.

(then it shows a 3x3 square of zeros with a 9 denoting the number of zeros.)

"Another example is 16. You can arrange 16 objects in the shape of a square with 4 rows and 4 columns. Thus, 16 is 4 squared."

(same thing as last square, instead of 9, with 16 zeros arranged in a square)

"The Greeks found an interesting relationship between Gnomon numbers and square numbers. They saw that if you add one gnomon to the next gnomon, starting with 1, you get a square."

(the diagram shows first one zero, then 2x2 square of zeros, and then a 3x3 square of zeros, and then a 4x4 square of zeros. underneath is written: 1, 1+3=4, 1+3+5=9, 1+3+5+7=16)

"Each time you add another Gnomon, you get another square. In other words, when you add Gnomon numbers in the order of increasing size, you get square numbers."

Okay i am done quoting. I just want to add my two cents and that will be it....

I think this definition is a much better definition, because it is a laymans explanation of something that quite simply is a layman's subject. a visual technique for squaring numbers should be relatively simple and easy to understand, but I continually find that wikipedia's mathematics articles are really poorly written. the idea of having this material is not for people who already know it to reference it, but rather to make information available to people who would like to learn it. From the way Gnomon numbers are portrayed here, it appears that it was a fairly simple concept. i propose instead of having a 9x9 square demonstrating every gnomon from 1-8, it just has the gnomons of one two three and maybe four like it is explained here. I find what makes mathematics sometimes difficult to understand is not the concepts themselves, but the people doing such a poor job of relaying the concepts. math problems and math articles should be more inviting, easier to understand, and more intuitive, that way all people can get a taste of math in their own way. also, more visuals need to be incorporated, and submitting images and visuals needs to be easier to do. by the way, i am not a proponent of dumbed down mathematics, but i am just saying this for the purpose of this forum. I was logging on Wikipedia in high school and i want people to continue to do so for answers to all their needs. —Preceding unsigned comment added by 76.28.40.216 (talk) 20:29, 22 December 2009 (UTC)