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Catching Elephant is a theme by Andy Taylor
(Source: teratogonus)
“It’s ironic that fractals, many of which were invented as examples of pathological behavior, turn out to be pathological at all. In fact they are the rule in the universe. Shapes, which are not fractal, are the exception.”
—- Mandelbrot, Benoit, mathematician born in Warsaw, fractal geometer.
(Source: mandelbrot-portraits.deviantart.com)
THE TRUTH.
(Source: hoiboy)
Mathematical induction proves statements.
In the past I was taught these steps:
* Show n = 1
* Assume for n = k
* Show n = k + 1
* Then the statement must be true for all n >= 1
But I just memorized them. I was never taught why; I just accepted it as true. We know it can work, of course. But why did we decide one day that this works; and why does it make sense? (Algebraically, geometrically, logically or with calculus?)
( I am not o.k. with just memorizing this. )
This might sound silly, but I’m not sure what to do.
Solve the differential equation
dy/dx= x*y^2
I was like, okay, I need to move the x’s to one side and the y’s to the other side.
Which left me with dy/y^2 =x dx
When you take the integral of each: the dy and dx go away.
Gah, I don’t know.
CITATION ( source) :
Nelsen, R. B. Proofs Without Words: Exercises in Visual Thinking. Washington, DC: Math. Assoc. Amer., 1997.
I did the work, I just want to know if my proof is good enough. The question is shown.
Dan Meyer is a high school math teacher in California. He explains that modern-day math textbooks scuttle inquiry and analysis in favor of teaching kids rote ways to solve problems—without actually learning anything.
Another part of the problem is that kids don’t seem to care about math, an issue that sometimes continues into an adulthood. ” Math makes sense of the world, math is the vocabulary for your own intuition.”
In teaching remedial math at his high school in Santa Cruz County, Meyer rewrites state-approved math word problems to obscure information until students think to ask for it. He also adds multimedia, like video, to his lessons to show his kids how math underlies just about everything they observe and do.
The way math is taught in the U.S. creates:
I’ve seen this in my friends, in my family, and even in myself growing up until I got to calculus and I opened up my mind.
People: Is there any day where you're not doing math homework?
Me: No.
Me:
People:
Me:
People:
Me:
People:
Me:
People:
Me:
People:
Me:
People:
Me : Integrals, integrals, integrals... Rolling around an axis of rotation and creating a solid. Let's calculate the volume. Happy freaking fun time.
[Wake up + Take a shower+ get ready for school + go to school early via bus + work on homework + go to class+ do class activities + class is over + take bus home + do more homework + study + do more homework until you decide to go to sleep ]
Repeat.
I just need help simplifying this to a u not y equation. Any ideas?
Integral of [ y * sqrt(6 + 4y -4y^2) ] dy
Trying to make u = 6 + 4y -4y^2 gives a du= 4 + -4y^2 , and that’s a bit messy.
