Comments on: Second grade squares http://osteele.com/archives/2005/12/second-grade-squares Languages of the real and artificial. Thu, 12 Feb 2009 00:20:28 +0000 hourly 1 http://wordpress.org/?v=3.0.5 By: Bret http://osteele.com/archives/2005/12/second-grade-squares/comment-page-1#comment-164 Bret Mon, 19 Dec 2005 09:24:37 +0000 http://osteele.com/2005/12/09/second-grade-squares#comment-164 Heh, I remember reading that way back then, but perhaps I was too taken by your mastery of OmniGraffle to remember the content. ;) Rereading it, it reminds me Oliver Byrne's rendition of Euclid's Elements ( http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.html ), which Edward Tufte referenced in one of his books... Heh, I remember reading that way back then, but perhaps I was too taken by your mastery of OmniGraffle to remember the content. ;) Rereading it, it reminds me Oliver Byrne’s rendition of Euclid’s Elements ( http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.html ), which Edward Tufte referenced in one of his books…

]]> By: Oliver http://osteele.com/archives/2005/12/second-grade-squares/comment-page-1#comment-163 Oliver Mon, 19 Dec 2005 05:58:53 +0000 http://osteele.com/2005/12/09/second-grade-squares#comment-163 Thanks, Bret. You're right about the labels on the arrows --- I've fixed them. I've actually got a picture of the visualization you're suggesting <a href="http://osteele.com/archives/2004/12/visualizing-basic-algebra" rel="nofollow">here</a>. When I started explaining squares to the seven-year-old this year, I <em>almost</em> printed that posting out, so that I could use it again. But we ended up going down a completely different path. That's one of the things I love about explaining things to people: even if I think I understand the material before-hand, I never end up taking the route I thought I would, when I'm traveling with someone else. Nice web site, by the way! Thanks, Bret. You’re right about the labels on the arrows — I’ve fixed them.

I’ve actually got a picture of the visualization you’re suggesting here. When I started explaining squares to the seven-year-old this year, I almost printed that posting out, so that I could use it again. But we ended up going down a completely different path. That’s one of the things I love about explaining things to people: even if I think I understand the material before-hand, I never end up taking the route I thought I would, when I’m traveling with someone else.

Nice web site, by the way!

]]> By: Bret http://osteele.com/archives/2005/12/second-grade-squares/comment-page-1#comment-162 Bret Fri, 09 Dec 2005 07:46:26 +0000 http://osteele.com/2005/12/09/second-grade-squares#comment-162 On the triangle in the big pink circle, shouldn't the horizontal arrow be labeled "-10", and the vertical arrow "-9"? Also, another way to visualize the relationship might be to use the grid in your first figure. To get the area of 9x9, start with the 10x10 square, subtract out the nine unit squares on top, the nine to the left, and the one in the corner. Also... that's a clever 7-year-old! :) On the triangle in the big pink circle, shouldn’t the horizontal arrow be labeled “-10″, and the vertical arrow “-9″?

Also, another way to visualize the relationship might be to use the grid in your first figure. To get the area of 9×9, start with the 10×10 square, subtract out the nine unit squares on top, the nine to the left, and the one in the corner.

Also… that’s a clever 7-year-old! :)

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