Wednesday, June 1, 2011
Pascals Hint
The question has arisen for those of you who have not found the formula for Er(n) whether to go ahead and write up your IA with the work you've done. I asked for guidance from some of my IB gurus and they said "don't have them write it up without the formula". They also said this:
If I give you hints but you write it up, it can still be considered your work.
If I straight up give you the answer, then presumably it cannot.
So here are my strongest hints which I hope you will find enlightening. Lacsap is Pascal spelled backwards. There is a famous triangle that Blaise Pascal explored that has lots of interesting patterns. I think you will find the numerator pattern if you explore Pascal's triangle. Try this website:http://www.mathsisfun.com/pascals-triangle.html For the denominator take a look at the pattern that is created by r(n - r). Coupled with your results for the numerator, you may find what you're after.
Please email me if that doesn't help,
Mr. Alei
If I give you hints but you write it up, it can still be considered your work.
If I straight up give you the answer, then presumably it cannot.
So here are my strongest hints which I hope you will find enlightening. Lacsap is Pascal spelled backwards. There is a famous triangle that Blaise Pascal explored that has lots of interesting patterns. I think you will find the numerator pattern if you explore Pascal's triangle. Try this website:http://www.mathsisfun.com/pascals-triangle.html For the denominator take a look at the pattern that is created by r(n - r). Coupled with your results for the numerator, you may find what you're after.
Please email me if that doesn't help,
Mr. Alei
Fractal Resources
This post is dedicated to links and information about fractals, one of the most amazing ideas in geometry.
Overviews:
Nova program: A great video introduction. About an hour.
Companion website: Some nice activities and background.
Software downloads:
Great programs from The Fractal Foundation: Links to various fractal software – mostly free. I recommend XaoS as a starting point.
Fractal Explorer: Like the name says, a fractal explorer. Interface is less intuitive than XaoS, but it has a few more features. No link on the FractalFoundation site.
More Fractal Software: Another compilation of a boatload of fractal generating software.
Information:
The Fractal Foundation: Based in Albuquerque. Jonathan Wolfe director. Educational & promotional content, activities, lots of links and info.
A Complete Online Fractal Course: From the Fractal Foundation - very informative.
Skytopia: British. David White. Great intro and detail on cutting edge 3D activity. 3D Mandelbulbs and some awesome pictures.
Mandelbrot Orbits:Something I put together from Geometer's Sketchpad. See also the Periodic Orbits section of this.
Discussions:
FractalForums: What seems to be the preeminent fractal discussion forum.
Animations & Art:
Rena Jones - Open me slowly
Slideshow: One of many cool YouTube slideshows of fractals set to music. Explore YouTube – there are hundreds!
Videos: A set of amazing 2 and 3D animations.
A cool Mandelbrot zoom
Overviews:
Nova program: A great video introduction. About an hour.
Companion website: Some nice activities and background.
Software downloads:
Great programs from The Fractal Foundation: Links to various fractal software – mostly free. I recommend XaoS as a starting point.
Fractal Explorer: Like the name says, a fractal explorer. Interface is less intuitive than XaoS, but it has a few more features. No link on the FractalFoundation site.
More Fractal Software: Another compilation of a boatload of fractal generating software.
Information:
The Fractal Foundation: Based in Albuquerque. Jonathan Wolfe director. Educational & promotional content, activities, lots of links and info.
A Complete Online Fractal Course: From the Fractal Foundation - very informative.
Skytopia: British. David White. Great intro and detail on cutting edge 3D activity. 3D Mandelbulbs and some awesome pictures.
Mandelbrot Orbits:Something I put together from Geometer's Sketchpad. See also the Periodic Orbits section of this.
Discussions:
FractalForums: What seems to be the preeminent fractal discussion forum.
Animations & Art:
Rena Jones - Open me slowly
Slideshow: One of many cool YouTube slideshows of fractals set to music. Explore YouTube – there are hundreds!
Videos: A set of amazing 2 and 3D animations.
A cool Mandelbrot zoom
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