[Edu-sig] Too simple (was Re: Interesting "gotcha")

[kirby urner]

I've always been a fan of Sesame Street, some of the earliest
episodes of which you can't buy as a minor they tell me,
because they show kids doing too dangerous things (like
making friends with strangers and running through a junk
yard, hopping on bed springs or something).  TV-14?

On that show, very disparate artists get a crack at sharing
about the Letter A or the Number 6.  Claymation.  Puppets.
Computer graphics.  Psychedelic.  Even demented.

If it's a style you don't like, not to worry, as clips are short.

You get to sample.

That's how I like a lot of math topics to get served, so
"customers" find a diet they not only can stomach, but
relish and wish to have more of (like "mindless consumer
but not mindless" is the marketing slogan).

I'm like the math teacher who changes the text book
every week, and then goes over the same topics, saying
"now lets see how *these* authors handle this subject
matter".  Or:  "lets watch another Youtube about
cosine, this one starring Britney Spears, formerly
of the Micky Mouse club"  (kids:  yaaaay).

http://www.youtube.com/watch?v=EQtyJZhV2lQ
(another logician featured)

I'm really into polyhedrons and if none of the clips have
them, within a radius of 30 minutes either direction on
the recording, then I'm likely to think only idiots would
watch this and tune out.  But that's just me.  I'll find my
niche, my like minded, and bliss out, twirling that
volume 5 rhombic triacontahedron long into the night,
marveling at all those beautiful ratios (proportions).

So my Python not surprisingly tilted towards VPython
in much of my writings and slideshows (from visual import *).
You'll see other themes as well.  Basically it's all Geometry
or Geography for me (like on mathfuture), keeps it neat and
easy, Occam my barber too.

Kirby Urner
4dsolutions.net/ocn/cp4e.html

On Wed, Mar 30, 2011 at 11:57 AM, Edward Cherlin <echerlin at gmail.com> wrote:

> Einstein probably did not say, "Everything should be made as simple as
> possible, but _no simpler_." However, somebody did, and somebody was
> right. One of the biggest problems in teaching programming is the
> constant pretense that we are not doing complicated mathematics, and
> the resulting attempt to hide the math.
>
> There is a lovely little book called Mathematics Made Difficult, whose
> premise is that refusing to tackle topics of modest complexity makes
> understanding far more difficult. With examples, of course.
>
> I have a similar complaint about freshman college physics courses that
> attempt to get by with no calculus.
>
> One of my favorite matth examples is how the use of elementary
> differential equations and Taylor series simplifies the definition of
> trigonometry. Define the exponential function by the equation
>
> y' = y
>
> which says that the growth rate of the function is proportional to its
> current value. Bring in examples from compound interest, biological
> growth, inflationary cosmology,... The function we are looking for is
>
> exp(x) = sum_0^\infty (x^n)/n!
>
> or any multiple of it. If you know that d(x^n)/dx is nx^(n-1), then
> you can see that the derivative of the power series for exp is itself.
>
> Now solve
>
> y' = -y (negative of exp)
> y'' = y (hyperbolic sinh and cosh functions)
> y'' = -y (sin and cos functions)
>
> in the same way, and look at the relations among their power series.
>
> Now derive e^(i\pi)+1=0 from e^(i\theta) = cos \theta + i sin \theta,
> which follows directly from the power series above, and then switch to
> linear algebra to get the sum, difference, and other formulae, and
> geometry to get the solutions of triangles.
>
> If anybody has difficulty with any of this I can point you to
> textbooks using these methods.
>
> If you would like a bit more of a challenge, we can do this all over
> again in elliptic and hyperbolic geometry, where we don't have similar
> triangles. ^_^
>


> --
> Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
> Silent Thunder is my name, and Children are my nation.
> The Cosmos is my dwelling place, the Truth my destination.
> http://www.earthtreasury.org/
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