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Archive for the 'Mathematics' Category

Matrices for programmers

Following the fine tradition of the colour theory post, you are getting another crash course. This time, a lesson in matrices. You’re going to be fine. And yes, I’ll hold your hand while you do this. *smile*
For those who are mathematically inclined, we’ll be working in the realm of real numbers (which I talked about [...]

Puzzle of 7 points and 6 straight lines - 2nd solution

This is the second solution to this puzzle: Construct a geometric shape with 7 points such that there are 6 straight lines, and each line must pass through 3 points. The first solution was already discussed last week.
And here’s the construction:

The 7 points are labelled A to G. The 6 lines are ADB, AFC, AGE, [...]

Puzzle of 7 points and 6 straight lines

My friend presented me with a puzzle: Construct a geometric shape with 7 points such that there are 6 straight lines, and each line must pass through 3 points.
My friend came up with a solution, but he wasn’t sure, so he consulted me. Actually there was a “model” answer, but he wanted to find another [...]

The barber paradox

Suppose there’s a barber who shaves only those who do not shave themselves. The question is, does the barber shave himself?
That was the question I posed in a previous article. The hint to the answer was actually given in the article: “What if your original assumptions were wrong?”
So let’s begin, with two fictitious men, John [...]

Fibonacci sequence and Golden Ratio

I haven’t written a math-related article in a while, so in this article, I’ll tell you about the Fibonacci sequence, the golden ratio and some associated program code.
Say you’re given this math formula, and told to find what the nth term is.
F(n) = F(n-1) + F(n-2)
where F(1) = F(2) = 1
Wow, initial conditions are given, [...]

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