This was the second week of geometry (following on from straight lines last week) and we looked at some of the properties of circles.
I talked briefly about the background of circles and geometry, in particular, how the circle was once seen as a divine shape and that the assumption was that planets moved on circular orbits and so on. We talked about the mathematical constant \(\pi \) (pi) and I a played a short Numberphile video with Simon Singh:
After that it was down to business with deriving the cartesian equation for a circle with centre at \( (a,b) \) and radius r : \[ (x-a)^2 + (y-b)^2 = r^2 \]
We looked at some simple geometry exercises which involved finding intersection points between circles and lines. It's a useful topic and draws on everything the students have done since Week 1 of the course.
This was a practice session for the students - a chance to discuss the lecture material and to try practice problems about circles and lines (e.g., how to find a tangent to a point on a given circle).
These two sessions were a review of the geometry topics studied so far. The emphasis was on practising exam type questions under some time pressure.
No teaching next week; the students are doing mid-term exams. Lots of marking for me!
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Dr Adrian Jannetta. Amateur astronomer, maths teacher and science enthusiast.