How Beautiful! 

Väldigt vackert när det är Mondrian målning som reflekteras om. Wow! Jag undrar hur en “grid” av rutor 1x1 skulle se ut efter den blivit omgjord.  Dags att uppgradera mina programeringsskills och göra egna program.. :)

Edit: Malin hade gjort ett fint program redan för detta. MEN, att rita raka stäck med mus är sådär halv lätt.. Resultat : 

When reflecting a painting in a circle, pen strokes close to the centre of the circle become thicker. Reflecting a pixel-based image would enlarge and distort some pixels.  A painting built of strokes, like a Mondrian-painting, is better suited for circle inversion.

 Paint Circle-Inverted Mondrian:

http://www.malinc.se/m/InvertedMondrian.php

This slide is really something! :)

Video of my talk last week at ICERM, where I discussed a bit of my process for making GIFs. You can also access my slides here.

Regolo’s Square Fractal

Inspiration: http://regolo54.tumblr.com/post/150627614707/fractal

Code as is.

Interactive code. Up/down/left/right mouse controls the size and placement of the squares. Up/Down arrows control how many squares are in each ring. Any other key will save the frame as a picture!

Wow, huvudmaskinen får jobba hårt när jag tittar på dessa. Kommer genast till funderingen över hur många varv den innesta behöver snurra för att alla skall vara tillbaka på start igen. Häftigt, ser skevt ut när varannan form är svart som bakgrunden. :) Riktigt bra jobbat med sidan och de du skapat i Geogebra!!

Distorted epicycloids and hypocycloids rolling inside other distorted epicycloids and hypocycloids.

Interactive versions with distorted and non-distorted versions, and the math behind it: http://www.malinc.se/m/RollingHypocycloids.php

So I just finished my CALC 2 class with the highest marks in the class and I wanted to put together a “guide” on how to study for calculus. It doesn’t matter if you are taking AP Calculus or Calculus in college, this guide should be a general overview but I will mention some specifics to AP Calc. *Picture from my Calculus lecture. 

General Tips

Buy the AP CALC review books. Regardless of whether you are in college calculus or actually in AP Calculus, the review books are great in condensing materials and having good examples. 

Create your own cheat sheet. Every time you learn a new formula or theorem, write it down in a cheat sheet. This forces you to recall the information constantly.

Know your common derivatives and common integrals like the back of your hand.

Fundamental Theorem of Calculus, Part I & II? Yeah, it’s fundamental. Need to know that. 

Common limits? Yep, that too. 

Know your pre-calc and algebra by heart. The hardest thing about calculus is not the formulas and theorems, but recalling past materials to solve a problem. If you could easily recognize trigonometric identities, you would be well set for the class.

Know what trig graphs look like and what they approach, etc. 

Learn how to do the math without a calculator. Some professors don’t let you use calculators on the tests and when you are become too dependent on the calculator, you tend to forget how to do simple addition/subtraction and multiplication/division. Also, there is a non-calculator portion to the AP Calculus Exam, so don’t make your calculator your crutch.

Practice every day + do your homework. A little practice everyday goes a long way and doing your homework (even if it doesn’t count as a grade) can be a drastic way of improving your grades because chances are, your teacher knows you probably aren’t going to do the homework and will have test questions very similar to the homework questions. 

Show all your work. Write all the steps out. If you make a mistake mentally, your whole answer will be wrong. To decrease the chances of loosing points for careless errors, label everything, even if it tedious. Also, work shown can count towards partial credit on tests. 

Practice the problems from your textbook + problems outside your textbook.

Understand and review old tests. When you get your tests back, redo the whole test on another sheet of paper. Try to understand where you went wrong. Was it a simple math calculation error? Did you do the derivative wrong? Was the theorem wrong? Did you forget a step like checking for conditions to apply L’hopitals Rule or Alternating Series Test for Convergence? Whatever it is, go through the entire test (yes, even the ones you got right) and re-do it. 

Ask for help when you don’t understand something. Solving tough calculus problems are easier when working with a group on a white board because you get a fresh set of eyes and a new mindset/approach to a problem. If you cannot tackle a problem, regardless of how many ways you have tried, it’s best to ask someone who already knows how to do it. 

Resources for AP CALC

Buy review books. Honestly, this is self-explanatory. I usually would go with a Barron review book, but hey, what ever works with you. 

Do the previously released AP Calc exams. If you are a BC student, do the release exams for both AB and BC for more practice. 

Previously released AB Exams

Previously released BC Exams

Step-by-step explanations for free response questions release

AB Study Guide

Cheat Sheets + Other Resources

I advise you to print out the cheat sheets and place it in the front of your calculus binder/notebook or where it can be easily accessed. 

Cheat Sheets

AP Calculus Stuff You Must Know Cold 

This 2-page cheat sheet is honestly god gifted and I advise you to print it out and laminate or something and put it in the front of your calc binder/notes. Will definitely save your life. 

Algebra Cheat Sheet 

Trigonometric Cheat Sheet

Calculus Cheat Sheet

Derivatives and Limits

Integrals

Online Tutorials + Videos

Khan Academy

Differential Calculus

Integral Calculus

Paul’s Online Math Notes

HippoCampus

Online Calculators

Symbolab’s Calculus Calculator

The most beautiful thing to ever exist when you are checking your answers or looking for the steps on how to do a problem.

Don’t rely on it too much. Actually learn how to do it. 

Wolfram Alpha

Implicit Differentiation Calculator

Desmos Online Graphing Calculator

Bet you don’t know how to graph an x-function on that TI-84 without solving it out for y. But it’s cool, neither do I. That’s why I rely on Desmos’ Online Graphing Calculator.

One of my favorite gifs of all time!!! 

periods

Got two Mongolian friends here at work if you want me to ask them? :)

Here’s my first attempt at Mongolian calligraphy.

I would greatly appreciate feedback.

This somehow reminds me of: http://www.derekhugger.com/merlot.html Hope you like it.

Breathe.

Welcome to my world of dyslexia... :)

When I'm halfway through a sentence and suddenly realise there is no way out of the grammatical crater I have dug myself

Neet way to learn matrixmultiplication!

An interactive matrix multiplication calculator for educational purposes

matrixmultiplication.xyz

“One day it just snapped in my mind how the number of rows of the first matrix has to match the number of columns in the second matrix, which means they must perfectly align when the second matrix is rotated by 90°. From there, the second matrix trickles down, “combing” the values in the first matrix. The values are multiplied and added together. In my head, I called this the “waterfall method”, and used it to perform my calculations in the university courses. It worked.”