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TAG: maths
The cos rule without cos
Ever since I first learned it, I’ve always loved the cos rule. It says that if a triangle has two sides a and b, with an angle of C between them, then the remaining side c can be found in this way: c2 = a2 + b2 – 2ab cos C.
The reason I like it […]
Pi, Tau and Eta
Recently, I’ve heard a lot about the number τ, and I find the whole thing a bit odd.
Here’s how it goes:
The number π is the ratio of a circle’s circumference to its diameter. It’s been known about for thousands of years and is an extremely useful number which appears in all sorts of unusual and […]
Rule collision
The same experience has happened to me several times in the Maths Drop-In Centre recently — with different students from different courses — and it was such a strong pattern I need to talk about it.
The students are doing some algebra involving negative powers on the tops of fractions. Something like this:
Now they remember this […]
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Not quite the bisection method
In various first year maths courses here, the students learn the “bisection method” for finding zeros of continuous functions. (A zero of a function is a number that makes the answer of the function come out to zero — it’s therefore also a point where the graph of the function crosses the x-axis.) It’s based […]
Four Triangles and Three squares
The picture here holds something really cool:
To make a picture like this, you begin with a triangle, then you construct a square on each side (like with Pythagoras’ Theorem). After that, you join the corners of the squares together to produce three more triangles. So in the end you have four triangles — which I’ve […]