# Math

## J-Pole Antennas for Ham Radio

If you’ve read any of my other posts, you know I love to build, tinker, and hack at stuff. Antenna-building is something I’ve not made a foray into, until recently. I have a dual-band handheld radio for the 2m and 70cm bands. The so-called rubber-duck antenna that comes with it performs ok but it isn’t ideal. I could get into my local repeaters which are about 10mi away with enough power to break the squelch, but my audio was weak…

To many, integral and differential calculus may as well be a foreign language from an alien planet. Many people don’t grasp the fundamental concepts which drive the calculus, and consequently fail to derive the value they otherwise could from that knowledge. I’ve always found the key to making use of some bit of knowledge is to internalize it, to restate the concepts in terms that are familiar and comfortable to you, but to compare this restatement and internalization to the…

## Neural Networks and How They Work

AI or Artificial Intelligence has been making headlines the world over the past few months. It’s time we all learn a little about how AI began and what role neural networks plays.   Artificial intelligence, also sometimes referred to as machine intelligence (MI), is a burgeoning field of Computer Science which has ties to many, many other fields. AI is the application of neural networks in various forms to allow a machine to imitate or give the impression of natural…

## Reliably identifying discrete colors from an RGB color sensor

For my Capstone Design project, one of my many tasks was to identify discrete colors on painted blocks (red, green, blue, yellow) using a the TCS34725 color sensor. I configured the color sensor to pass back four 16-bit integers representing the RGB and Clear color values of the reflected object that the sensor is “looking” at. Initially, I tried a simple linear matrix equation to map the input RGBC values to RGBy output numbers. I then took the highest output value…

## Interesting Numbers

The Fibonacci sequence is one of the most widely used sequences when introducing the concept of sequences. The sequence is defined as the following: FN = FN – 1 + FN – 2 So, starting with F0 = 0 and F1 = 1, the first few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … and so on. An interesting thing to note about the Fibonacci sequence is that the ratio of one Fib number to its predecessor…

## Toom-k Polynomial Multiplication

I’ve been pretty busy with classes the past two weeks, but I’ve learned a few neat things and I’d like to share one of them. Multiplying big numbers is a problem when the numbers are really, really big. How big is really, really big? Depends on the hardware your using. But to multiply really big numbers, we represent the two multiplicands as polynomials where each term is in the form cxn, where x is the base in the number system, c is its coefficent modifier…

## Look and Say Numbers Sequence

The very famous John Conway (Conway’s Game of Life) discusses a silly ‘look-and-say’ math trick that I’ve been playing on people since middle school. Who would have guessed such interesting characteristics could come of this sequence? I am inspired by John Conway’s insight into things as simple as this basic sequence. See the video below: