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### Course: Math for fun and glory>Unit 1

Lesson 9: Other cool stuff

# Fractal fractions

How to make snazzy-lookin' fractal equations using simple algebra. For more abacabadabacaba: http://www.abacaba.org/ and http://books.google.com/books?id=QpPlxwSa8akC&pg=PA60&lpg=PA60&dq=abacabadabacaba+%22martin+gardner%22&source=bl&ots=92eAyvrZGV&sig=J2uvF2DAyn9kY8nSarSy-XIXW74&hl=en&sa=X&ei=Np45T4K9GYixiQK92NG2Bg&ved=0CCEQ6AEwAA#v=onepage&q&f=false. Created by Vi Hart.

## Want to join the conversation?

• At , why do binary trees appear so often in math?
• That's a very good question. I seem that trees in general, not only the binary kind, appear so often in math, derived sciences (eg, computer science) and, in general, rational thinking (eg, logistics or management). It's probably related to a typical way human beings (or mammals in general?) think rationally: complex problems or situations are decomposed into simpler units and this, in turn, are further decomposed and so on, recursively. Obviously this can be visualised (and formalised) via tree structures. As another example, humans (and probably other organisms) like to classify a lot, so that, for instance, they can describe Snoopy as a particular beagle, beagles as particular dogs, etc. The power of such generalisation/specialisation mind activity should be quite clear (http://en.wikipedia.org/wiki/Ontology_%28information_science%29)
• ...does this have anything to do with the Wau video she did a little while ago..?
• These videos are not in series, but because math is always connected to itself, strage similarities will pop up.
(1 vote)
• what does the root word bi in binary exactly mean?
• bi means two like bicycle-meaning two wheels or bifocals-meaning two different lenses
• From to , how does Vi get all those letters of abaca....?
abaca... {Argh! I still can't spell it!}
• Practice makes perfect! I can say up to L!
• At , couldn't x also be -5?
What's written is:
x = 17/x + 8/x = 25/x
x^2=25
x=5,
but I disagree with the last step. You can start with -5 and still get the fraction.
-5
= -5
= 25/(-5)
= 17/(-5) + 18/(-5)
= 17/(17/(-5) + 18/(-5)) + 18/(17/(-5) + 18/(-5))
= 17/(17/(17/(-5)+18/(-5))+18/(17/(-5)+18/(-5)))+18/(17/(17/(-5)+18/(-5))+18/(17/(-5)+18/(-5)))
= 17/(17/(17/(17/(-5)+18/(-5))+18/(17/(-5)+18/(-5)))+18/(17/(17/(-5)+18/(-5))+18/(17/(-5)+18/(-5))))+18/(17/(17/(17/(-5)+18/(-5))+18/(17/(-5)+18/(-5)))+18/(17/(17/(-5)+18/(-5))+18/(17/(-5)+18/(-5)))) =
and so on. So for each fraction which has lost its denominator, it seems like there are two solutions.
• Yes, for this particular fraction, there are two solutions.
• in , can you make it until 'z' with using all the alphabets in a row?
• You can, but it would be very long (67,108,863 letters).
(1 vote)
• how do you do 8 square root 13 on a calculator?
(1 vote)
• That would vary depending on the type of calculator, you should google that.
• hey guys, for some reason I can't get energy points by watching videos anymore. can someone tell me why?