An Imaginary Tale: De Moivre’s Formula in a Gif

I’ve been reading the book, An Imaginary Tale: The Story of i [the square root of minus one] by Paul J. Nahin and it’s really interesting!  I’m almost to chapter 4 and so far it’s been introducing some nifty ideas about complex numbers.  Among the content, we find a very convenient way of calculating the value of a complex number when multiplied by itself an integer amount of times.  That is, $z^n=(a+bi)^n=r^n \cdot \left[ \cos\left(n\theta\right)+i\sin(n\theta)\right]\mid n\in \mathbb{Z}^+$.  This is De Moivre’s Formula.

Caffeine + Low Blood Sugar = Shakiness(Parkinson’s)

As a medically induced diabetic who drinks coffee, I can say this. LOL

Creativity Meets Math

Screen capture using Circular Design Maker

Ever wonder if there’s any creativity in logic and math?  Do left-brained people struggle to be creative?  Where does creativity and logic come from?

Try out my Circular Design Maker.
* This seems to work better with the Mozilla Firefox browser

I was curious what it would look like if rotated rotating points around center points around another center point.  LOL. Try saying that 5 times fast!

Using GeoGebra, I made this worksheet for us to see.

Try making some designs and take pictures of them!

Creativity and Logic come from Curiosity.

Hate Math Love My Glasses by roxagrama

Hate Math Love My Glasses by roxagrama

I happened to find this on Deviantart.com. This piece comes from roxagrama on Deviantart.   Although it has an ironic name, I think it shows a nifty perspective through the eyes of a mathematician.  Love it!  I’m curious what the formulas are describing?

Why Do We Need Math?

I know this is probably more of a reblog but I felt it was really important to show math students and teachers. Carl Sagan makes great points about who will be calling the shots in your life and in the real world when it comes to Science and Technology and this clip is less than 3 minutes long.

How to Calculate the Value of e

ver wonder how the calculator seems to know the numeric value of $e$ ?  How could it possibly know?  $e$ is an Irrational Number which means its decimals don’t repeat! (Specifically $e$ is a Transcendental Number but it falls under the category of an irrational number).  So how can you fit an infinitely large number in a small box?  Or for that matter, how did Leonhard Euler manage to calculate $e$ to 23 decimal places without a calculator?

Math – You Haven’t Seen The Last of Me

Hi everyone!  I just wanted to bring your attention to a new page I added to MathyNick.com.  In the Printables tab is a collection of PDF Mathematics handouts/packets that I’ve collected over the years of being a tutor.  Look them over and see if you find any that look like they can help you.

In my last post, A REALLY Brief Intro to Complex Numbers, I talked about a few necessary definitions to know what Complex numbers $\mathbb{C}$ are.  Complex numbers are really intriguing and necessary for our electronic devices to work.  You might be reading this on a computer, smartphone, tablet, etc., but none of the advances in technology would be possible without use of complex numbers.  Creating wonders from wonders.
Imaginary numbers and complex numbers interest me a lot.  Aside from the properties of infinity ($\infty$), complex numbers $\mathbb{C}$ are, well… complex! They’re very strange and yet they open a whole new world of numbers beyond the Real numbers $\mathbb{R}$.