Finally, I have a solution to Exercise 1.13:
http://www.kendyck.com/math/sicp/ex1-13.xml
Posted by Ken Dyck in Programming
April 24th, 2005
Solution to SICP Exercise 1.13
10 Responses to “Solution to SICP Exercise 1.13”
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Scott says:
Ken,
Well done — my wife and I each worked separately on this for half an hour with minimal progress. How long were you working on the problem?
Scott
(also working through SICP)
July 22nd, 2007 at 3:08 pm -
Ken Dyck says:
Actually, I found the toughest part about this exercise was formatting it for the web. Compared to getting MathML to work, the proof was relatively simple, but as I recall, that wasn’t entirely straightforward, either.
I’m sorry. I don’t remember how long I spent working on it.
Good luck with SICP, though. I have to say that it’s pretty cool (and rare) that you have a wife that is interested in this sort of thing. Good luck to both of you.
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Ran says:
Hi
Nice proof!
The main part of the induction can be simplified considiribly by taking into account the fact (which is mentioned in the book) that
phi^2 = phi + 1
and similarly for psi. Thus you have that
phi^(n+1) - phi^n - phi^(n-1) = 0
which you can compare on the right hand side to psi.
In fact, you don’t even have to “open” phi and psi! -
Bill Mill says:
Beautiful proof, it’s been four years since I thought about inductive proofs, and I followed you right through.
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Morgan says:
How can I view this? I have tried both Firefox and IE.
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Ken Dyck says:
Morgan, the proof is written in MathML.
Firefox has had built-in support for rendering MathML since version 1.5 from what I can tell. That is, it should ‘just work’. Perhaps you need to upgrade to a more recent release of Firefox.
IE requires a plug-in to render MathML. MathPlayer seems to be the most popular, but as a Firefox user I can’t attest to its quality.
Hope this helps.
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Jonathan Hartley says:
Hey. I have viewed the solution at:
http://www.kendyck.com/math/sicp/ex1-13.xml
in the past, but now when I go to look at it, it says:
Error loading stylesheet: An unknown error has occurred (805303f4)http://www.w3.org/Math/XSL/pmathml.xsl
Is this just me? Given the comments above, I’ll mention that I’m on Firefox 3.5.7, on Windows.
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Ken Dyck says:
As Jonathan points out, there appears to be a problem viewing the proof in Firefox 3.5.7. I’m also seeing problems in IE8 and Chrome 3.0.195.38.
It seems that sometime since the page was first launched, browsers have deemed it a security risk to fetch stylesheets from external sites. I’ll fix this when I have some time.
Thanks for reporting the problem Jonathan!
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Jonathan Hartley says:
n.p. I don’t know if you already fixed it, but today I’m at home (i.e. on a different computer, but still running Firefox 3.7.5) and it works fine. Hooray. Thanks.
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Ken Dyck says:
It is strange that it worked for you, Jonathan, because I hadn’t changed anything.
Anyways, it should be fixed now for anybody else who is having problems.