Numb3rs
This is a blog where a professor from Northeastern University's Math department posts mathematical comments on the television show "Numb3rs". To comment, write to bridger@neu.edu.
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October 31, 2005
Before moving on to discuss the mathematics of polar coordinates, I'd like to point out that there is a lot of math involved in analyzing the physics of radio signals themselves. As you probably know, "electromagnetic radiation" -- i.e. light, x-rays, microwaves (which include radar) etc -- can be thought of as "vibrating waves", usually represented mathematically as sine or cosine curves. These come in different frequencies and combinations of frequencies... continued »
October 29, 2005
In last night's episode, radar played a central role. There is a tremendous amount of mathematics involved in a modern Radar (= RAdio Detection And Ranging) system -- starting with very elementary ideas and ending with state of the art image-processing algorithms. I'll present some of the basics today and add more during the week.
First of all, let's start with a simple example of detection and ranging. Suppose you go out at night when a storm is threatening... continued »
October 28, 2005
This is a repeat. I wrote about "Squishing and Squashing" in the blog for May 8 (last spring) which you can look up on this site.
I am going to spend the next few blogs telling you about how mathematics is used in radar systems. This involves all sorts of stuff, from simple coordinate systems through trig and polar coordinates, through calculus and modern image-processing algorithms... continued »
October 27, 2005
Charlie says to Amita when she asks him about National Security Agency (NSA) codes: "If I told you, I'd have to kill you."
"No, seriously..." "Yes, seriously".
This is a bad joke; the lines are so hackneyed they don't even appear anymore on late night comedy... continued »
October 22, 2005
Well, not every show can have meaningful mathematics. It seemed to me that Charlie did a lot of scribbling and name-dropping, but didn't make a single useful mathematical contribution. The equations on the board seemed to be some sort of probability calculations, but there simply was not enough data to apply them to... continued »
October 20, 2005
Here is an example of a vector field (I'll post some more when I get a chance):
Picture of a 3-dimensional vector field
It was produced by a software program called Maple. It is the vector field which places the vector (x2 + y,3x + 4y,1) at the point (x,y,z).
October 19, 2005
While looking at the leak in Charlie's kitchen, Larry drops some ink from a pen into the puddle and talks a bit about "vector fields". What are they?
Well, for some things we want to measure, we need two kinds of information: their size or magnitude and their direction. One example is a force. The magnitude of the force is how strong it is; maybe this would be measured in pounds (or newtons in the metric system)... continued »
October 17, 2005
Well OK, I had a chance to look at a tape of Friday's episode. There were several items that I'd like to comment on.
We look in on Charlie "pruning a tree." What is that and what does it have to do with mathematics? A tree is a way of organizing data in the memory of a computer. Think of this memory as a bunch of mailboxes, each with an address. A mailbox contains data of some sort... continued »
October 13, 2005
In my last blog I mentioned spherical trigonometry as the field of mathematics used to calculate positions on the surface of the earth (navigation) or in the heavens (astronomy). This subject is not taught much any more in the US. Its two main fields of application, navigation and astronomy have become largely computerized: Global Positioning Systems (GPS) for the former and computer-controlled telescopes for the latter. Also, vector methods have replaced it in some applications... continued »
October 11, 2005
If you stick a vertical pole in the ground, its shadow will move as the day progresses. This is because the rotation of the earth makes the sun appear to travel across the sky. As the sun "moves", the shadow that a fixed object casts moves with it. This suggests that you could make a clock: simply draw a line from the pole along the shadow at noon: mark it with a "12"; then draw another line along the shadow at 1 PM and put a "1" on it; the line at 11AM is marked with an "11", etc... continued »
October 8, 2005
The October 2 blog contains a discussion of remote car-door controllers. In that blog I gave an example of how these controllers might generate the "secret codes" that enable them to unlock car-doors securely... continued »
October 5, 2005
The last contribution that Charlie makes to last Friday's episode is to identify which communication to a certain website is from the gamblers the FBI is trying to find. He does this (with Amita's assistance) by monitoring messages that contain gambling odds, which he identifies with "Farey fractions."
I like to think of Farey fractions as batting averages. The denominator is the number of times at bat and the numerator is the number of hits... continued »
October 2, 2005
Charlie's decoding of the remote car entry system is his most important contribution to last week's episode. Here are some of the issues related to these systems.
(a) Essentially, all the entry systems use the same frequency, so when a controller is operated, all nearby cars get the same message.
(b) It is obviously essential that each controller controls exactly one car... continued »
