66 posts
Latest Posts by mrvmt - Page 2
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
Time to take actions! We only got one place to call home, so lets act like its our home!
As governments discuss climate change in Paris, they’ll be referring to the dire predictions of climate scientists. Here are three visualizations of possible futures based on detailed climate models and summed up by the United Nations’ Intergovernmental Panel on Climate Change (IPCC) in their 2013 report. The deeper the red - the hotter things are getting.
The message is clear: we better act fast.
How did they come up with these models? Read or listen to Nell Greenfieldboyce’s story.
Image Credit: NASA’s Scientific Visualization Studio and NASA Center for Climate Simulation
Here’s the orginal creator, he’s a legend:
beesandbombs (http://beesandbombs.tumblr.com/)
Take care
Waving Circles
Remake of this awesome gif (does anyone know the original creator?): https://33.media.tumblr.com/a5d2523e8a4fc92e1629ae9937d870f6/tumblr_nl4lm8O73g1u93xcqo1_500.gif
This is early days for my conversion to p5.js. Here’s the code: http://jsfiddle.net/dandersod/8uL4s35d/
Damn, yes, why wouldn’t you! Looks great!
idk, why wouldn’t I make these and post them
Would like a map of the whole area, just to know for sure i’ve been to all the places :)
Wow, this is the coolest comic i ever read! Got your book (”What if?”) and now think its the second coolest thing i read! :) Keep it up!
Wow, this is the coolest comic i ever read! Got your book (”What if?”) and now think its the second coolest thing i read! :) Keep it up!
Oh, so your from Denmark then, or maybe its “Skåne” ? :)
Like your piece. With flowers and everything! :)
http://autolyses.tumblr.com/tagged/autou
some photos I’ve taken or things I’ve made, just for fun
This guy!
Big Brains. Small Films. Benoît Mandelbrot, The Father of Fractals
In his final interview shot by filmmaker Errol Morris, Mandelbrot shares his love for math and how it led him to his wondrous discovery of fractals.
Beautiful!
Double Arm
This sketch was made by rotating point 1 around a circle, rotating point 2 around point 1, and then joining a line between point 1 and point 2. In the gif point 2 is traveling in the same direction as point 1. Point 1 is traveling at 1x, and point 2 is traveling at 2x. Following the gif are some of my favorite combinations of the periods:
Rotating same direction:
1x and 1x
1x and 2x
1x and 5x
2x and 1x
2x and 5x
5x and 8x
The last image is an array of all the varieties from 1x to 9x for each point.
code: http://p5js.sketchpad.cc/sp/pad/view/jLceHatXid/latest
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
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
Hey all. Here in Sweden some of our preschools teaches signlanguage. It’s a really good compliment and the kids rock it like they never did anything else. I know Swedsh signlanguage because of my sisters deaf kid. Its a wonderfful way to communicate. Love the bodylanguage that comes with it! Take care!
Reblog if you think sign language should be taught as a language in schools.
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
Även efter man läst förklaringen och verkligen försöker bortse skuggans illusion, så stuttsar denna boll...
Skulle det fungera om man tog bort perspektiv rutorna? Så du inte har djupet att förhålla sig till?... Hmm
Shadow illusion
The human brain uses shadows to interpret how objects move. By faking the shadow, one can fake the perceived motion of an object. The red circle moves along a line.
Interactive version:
http://www.malinc.se/m/ModellingIllusions.php
This somehow reminds me of: http://www.derekhugger.com/merlot.html Hope you like it.
Breathe.
A sphere made out of straight lines! Beautiful!
Hypotrocoid
http://www.malinc.se/math/trigonometry/spirographen.php
Hej Malin. Hoppas du förstår svenska, annars kommer det på engelska under. Har du kvar koden till denna? Skulle så gärna vilja se en loop. dra ner hastigheten på den lite och se detaljerna lite mer. Tack på förhand!
Hey Malin. I hope you understand swedish, in otherwise i’ll write it in english below. Do you still got the code for this one? I would like to see it in a loop and slow down the speed a bit, just to see more details. Thanks in advance! Take care!
Tangent Circles
http://www.malinc.se/math/geometry/dothisen.php
Hey BAB, could you please share the code to this? Im on the way to learn some processing and this is the kind of code i would like to learn. So, please share, so i can learn from it :)
Take care mate!
rgb knot
Verkligen en vacker skapelse!
Golden rectangle
Back when I was in school, this concept was really hard for me to grasp my head around, and I must say, this was a compelling way to understand the function of multiplying with negative numbers!
Thanks!
By virtue of everyday usage, the fact that (-1) x (-1) = 1 has been engraved onto our heads. But, only recently did I actually sit down to explore why, in general negative times negative yields a positive number !
Intuition.
Let’s play a game called “continue the pattern”. You would be surprised, how intuitive the results are:
2 x 3 = 6
2 x 2 = 4
2 x 1 = 2
2 x 0 = 0
2 x (-1) = ?? (Answer : -2 )
2 x (-2 ) = ?? (Answer : -4 )
2 x ( -3) = ?? (Answer : -6 )
The number on the right-hand side keeps decreasing by 2 !
Therefore positive x negative = negative.
2 x -3 = -6
1 x -3 = -3
0 x -3 = 0
-1 x -3 = ?? (Answer : 3)
-2 x -3 = ?? (Answer : 6)
The number on the right-hand side keeps increasing by 3.
Therefore negative x negative = positive.
Pretty Awesome, right? But, let’s up the ante and compliment our intuition.
The Number Line Approach.
Imagine a number line on which you walk. Multiplying x*y is taking x steps, each of size y.
Negative steps require you to face the negative end of the line before you start walking and negative step sizes are backward (i.e., heel first) steps.
So, -x*-y means to stand on zero, face in the negative direction, and then take x backward steps, each of size y.
Ergo, -1 x -1 means to stand on 0, face in the negative direction, and then take 1 backward step. This lands us smack right on +1 !
The Complex Numbers Approach.
The “i” in a complex number is an Instruction! An instruction to turn 90 degrees in the counterclockwise direction. Then i * i would be an instruction to turn 180 degrees. ( i x i = -1 ). where i = √-1
Similarly ( -1 ) x i x i = (- 1 ) x ( -1 )= 1. A complete revolution renders you back to +1.
We can snug in conveniently with the knowledge of complex numbers. But, complex numbers were established only in the 16th century and the fact that negative time negative yields a positive number was well established before that.
Concluding remarks.
Hope you enjoyed the post and Pardon me if you found this to be rudimentary for your taste. This post was inspired by Joseph H. Silverman’s Book - A friendly Introduction to Number Theory. If you are passionate about numbers or math, in general it is a must read.
There are several other arithmetic methods that prove the same, if you are interested feel free to explore.
Have a Good Day!
PC: mathisfun
Wow, “ For a photon, its entire existence is instantaneous. “ , that put things in perspective!
Ask Ethan #109: How do photons experience time?
“[L]ight takes about 8 minutes to travel from the sun to earth. Light travels at the speed of light. If you do that relativity kicks in. So my question is, how much time passes for the photons traveling? In other words, how much have the photons aged when the reach the earth? Thanks for considering this.”
Travel at any constant speed, at rest, slowly, or near the speed of light, and you’ll experience time passing at the same rate it always does: one second per second. If someone else is moving relative to you, they’ll see your clock run slow (and you’ll see theirs run slow) depending on how quickly you move relative to one another. But what about a photon, which moves at the speed of light? From your point of view, no matter what your motion is, you won’t see time pass for it at all, and it won’t even experience time! For a photon, its entire existence is instantaneous.
Important topic!
Spread the word!
Science is being defunded around the world. Help us spread the importance of science, by sharing this video!
Despite our achievements, science and society are often at odds. Scientific discoveries like the Earth is round, that our planet revolves around the sun, or that diseases are spread through germs were all once ideas that were rejected by society. So much so that Giordano Bruno was burned at the stake for suggesting the Earth wasn’t the centre of the universe, and even Galileo was sentenced to house arrest for supporting the theory. Today we see the rejection of scientific evidence for vaccinations - leading to preventable disease like measles coming back, after being wiped out in the year 2000; or the rejection of scientific evidence for climate change, despite the vast consensus among scientists.
Let’s spread our love of science further, so others can learn to understand and appreciate it! Your sharing is appreciated
Numberphile (https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A) Got some good videos on the subject.
Heres one that introduce the topic: https://www.youtube.com/watch?v=aqyyhhnGraw
Did you know that there’s a whole branch of topology called knot theory studying knots?
Find out more here: https://en.m.wikipedia.org/wiki/Knot_theory
I wounder what the gif community could do with such a simple code! :)
Finally Vihart post a video again!
Down the rabbithole. :)
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