Math visualization: (x + 1)^2
billthelizard.com
Math visualization: (x + 1)^2
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Re: Math visualization: (x + 1)^2
#2That was pretty simple. See also this fun post of mine: http://www.jgc.org/blog/2008/02/sum-of-first-n-odd-numbers-i...
Re: Math visualization: (x + 1)^2
#3Cf. the binomial cube (http://homepage.mac.com/montessoriworld/mwei/sensory/sbinoml...), which has been part of Montessori preschool classrooms since, umm, probably since Maria Montessori herself was teaching them a hundred years ago. I think the Montessori cube was based on a similar object designed by Freidrich Fröbel, the man who invented kindergarten.
Re: Math visualization: (x + 1)^2
#4That was pretty simple. See also this fun post of mine: http://www.jgc.org/blog/2008/02/sum-of-first-n-odd-numbers-i...
I had also included that one in an earlier post: http://www.billthelizard.com/2009/07/six-visual-proofs_25.ht... (scroll down to the 5th "proof").
I think I like the image you used to visualize the relationship a little bit better than the one I used.
Re: Math visualization: (x + 1)^2
#5Here's all of permutations and combination (written in processing) in 3D space.
Permutations and combinations.
Taking 3 (visualized as dimensions) from 7 (length of side).
License: Public domain. Attribution requested.
KEY:
Permutation: (order matters).
Repeating (Sequence): All (little cubies). Eg: Passwords.
Non-repeating (Arrangement): All except the reds. (ie transparent + blues). Eg: Number of ways of podium finishes in a race.
Combination: Selection (order doesn't matter).
Repeating: Cubies with white outline. Eg: Number of 3 scoop icecream serving from a set of flavours.
Non-repeating (Subset combination): The blues. Eg: Number of ways to choose 3 member committies from a group.Re: Math visualization: (x + 1)^2
#6I have been collecting visual proofs for over a year now. I think I am gonna start writing an article series about math visualizations.
Re: Math visualization: (x + 1)^2
#7I have been collecting visual proofs for over a year now. I think I am gonna start writing an article series about math visualizations.
I keep meaning to write more of these too. My blog is (ostensibly) about programming, but I find that I keep drifting further and further into mathematical topics without tying them back into programming somehow. I should probably commit to one or the other, I just can't decide.
Re: Math visualization: (x + 1)^2
#8I use to wonder why there was an outside and inside part when doing FOIL. It was after that I saw the visual proof, and doing other types of multiplication with multiple 'parts/terms', that it slowly dawned on me that there's cross-components. It's the same sort of thing when you multiple matricies or covariances. You need the contribution from every combination of terms.
Re: Math visualization: (x + 1)^2
#9I have been collecting visual proofs for over a year now. I think I am gonna start writing an article series about math visualizations.
I keep meaning to write more of these too. My blog is (ostensibly) about programming, but I find that I keep drifting further and further into mathematical topics without tying them back into programming somehow. I should probably commit to one or the other, I just can't decide.
You don't need to. There are surprising connections. E.g. between partial differentiation and algebraic datatypes: http://en.wikibooks.org/wiki/Haskell/Zippers#Differentiation...
Re: Math visualization: (x + 1)^2
#10Earlier quoted context omitted.
I keep meaning to write more of these too. My blog is (ostensibly) about programming, but I find that I keep drifting further and further into mathematical topics without tying them back into programming somehow. I should probably commit to one or the other, I just can't decide.
You don't need to. There are surprising connections. E.g. between partial differentiation and algebraic datatypes: http://en.wikibooks.org/wiki/Haskell/Zippers#Differentiation...
I guess my third option is to concentrate more on finding those connections. Thanks for the feedback.