- Assignment 3 has been posted today. We discussed Problem 1 today. See the file 20190311_A2P2_A3.nb.
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In Problem 1 you need to use the Calendar package: Needs["Calendar`"]. This package contains several functions related to date arithmetic: DaysBetween[], DaysPlus[], DateQ[].
An important warning: Before you use the commands from the Calendar package you must load the Calendar package. If you by mistake try to use one of the Calendar package commands without having the package loaded, you will have to quit the kernel (Evaluation→Quit Kernel→Local) before loading the package. - I will comment on Problem 2 and Problem 3 in class.
- The files vonKoch_curve.nb and PythagorasTree.nb are "guides" for the construction of fractals in Problem 4.
- In the first part of Problem 4 you are asked to create a function that would produce iterations of the quadratic type 2 curve. In the first picture below I show the 0th iteration in blue and the 1st iteration in red. I emphasize the points that are used. You do not need to do this on your plots. In the second picture below I show the 1st iteration in blue and the 2nd iteration in red. The large picture is the fourth iteration of the quadratic type 2 curve.
- In the second part of Problem 4 you are asked to create a function that would produce iterations of the Cesaro fractal which depends on angle $\alpha$. The four pictures below show the 0th, 1st, 2nd and the 3rd iteration of the Cesaro fractal with the small angle $\alpha = \pi/16$.
- Below is an animated gif file that cycles through the 1st, 2nd, 3rd, 4th, 5th and the 6th iteration of the Cesaro fractal and, within each of the iterations cycles through all the angles starting from $\pi$, proceeding towards $0$ and then back to $\pi$ in steps of $\pi/50$. The animation starts by the first iteration and cycles through angles from $\pi$ to $0$ and back to $\pi$. This is repeated for 2nd, 3rd, 4th 5th and 6th iteration. For each iteration there are 101 pictures.
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Place the cursor over the image to start the animation.
- Assignment 2 is has been posted today. Comments about the problems are below.
- Very important tools in Mathematica and on this assignment are Module[] and Pure Function. We have seen examples of pure functions when we used FindSequenceFunction[] in Problem 3 on Assignment 1. I will talk about these two objects more in class.
- Problem 1 is an exploration of a surprising function. The point of the problem is to find accurate answers to the questions that are asked and support them with as rigorous explanations as you can. You should use what you learned in Calculus combined with the power of Mathematica. To explore the function use the functions D[] to find the derivative and FullSimplify[] to simplify it. To find special points you can use Solve[], Reduce[] or FindRoot[] where appropriate. However, Mathematica needs a lot of human help in this problem.
- Problem 2.
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In the first part of this problem you need to unify, as explained in the problem, three animations given below.
Place the cursor over the image to start the animation.
Place the cursor over the image to start the animation.
Place the cursor over the image to start the animation.
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In the second part of this problem you need to reproduce two pictures from Wikipidia's
Cardioid page
I made an animation that unifies these two pictures. You should be able to produce something like this. If not you can present one animation and one picture.
Place the cursor over the image to start the animation.
- In the third part of Problem 2 you need to produce generalized cardioids. The animations below are large. On a slow internet connection it takes a while for them to load.
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Below is the cardioid generated by a wheel with radius 1/2 rolling on a circle with radius 1.
Place the cursor over the image to start the animation.
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Below is the cardioid generated by a wheel with radius 1/3 rolling on a circle with radius 1.
Place the cursor over the image to start the animation.
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Below is the cardioid generated by a wheel with radius 2 rolling on a circle with radius 1.
Place the cursor over the image to start the animation.
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Below is the cardioid generated by a wheel with radius 3/2 rolling on a circle with radius 1.
Place the cursor over the image to start the animation.
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In the first part of this problem you need to unify, as explained in the problem, three animations given below.
- The file Probabilities.nb deals with questions which are similar to questions in Problem 3.
- I will comment on Problem 4 in class.
- Mathematica part of the class starts on Monday, February 11, 2019.
- The information sheet
- We will use
- To get started with Mathematica see my Mathematica page. Please watch the videos that are on my Mathematica page before the first class. Watching the movies is essential for being able to organize your homework notebooks well! I will not discuss the basics of notebook structuring.