Monday 18th February from 9:30 am to 4:00 pm (early arrival and late departure by arrangement).
Cost: £25 - bring your own lunch and snacks. Water, squash, tea, coffee, "milk and cookies" provided.
To be held at my house in Burgh Heath.
Maximum of six students, five places currently available.
Please contact me (see Home page for details) to reserve your space.
Visits prior to event welcomed (see Home page for contact details).
Years 12 and 13 welcomed. Knowledge of calculus (differentiation) and exponential(ex)/logarithmic graphs helpful.
Please note that this is not a "crammer" or revision day. It is a day of (hopefully) fascinating mathematically-based challenges that require knowledge up to 'A' level. These challenges will be of the "open-ended" variety that are closer to real-life mathematical problems and seem to be experienced only rarely in the school curriculum. Alongside this, maths puzzles and mini-challenges will be presented that will stimulate and exercise the finest of minds.
There is usually a best way of designing anything. Finding it is known as "optimising" and almost invariably requires differential calculus in order to obtain exact results. Paper and scissors will be used extensively as the we search for the cuboid, pyramid and cone with the largest volume that can be produced from a given piece of paper. The more complicated the shape, the more complicated the maths but (surprisingly?) the simpler the solution.
This starts from a simple question: "Can you predict the location of the crease when you fold a piece of paper?" Of course, this being a mathematics day means that we expect you to define the equation of the crease line. Origami paper is square and folds produce lots of right-angled triangles. That is where Pythagoras comes in. In what ratio are the lengths of the sides of these triangles? How could we produce a triangle with sides in a given ratio?
Jump out of an aeroplane and your downward speed increases until it reaches its terminal velocity. It is a good idea to open the parachute before you reach the ground. Once you open the parachute, your speed reduces exponentially towards a new, lower, terminal velocity. It is important that the speed on impact is less than that which would cause injury. But, suppose you are in a hurry? When is the optimum moment to open the parachute to get to the ground uninjured in the least time?
You are in the sea on a beautiful summer day. Suddenly, an ice cream van parks on the beach and you know that a queue will rapidly form. You need to get to the ice cream van as quickly as possible. But what direction should you head in? You know that you can travel faster on land than you can in the sea so going in a straight line from you to the van won't be the fastest route. Can you use your maths capabilities to work out the optimum direction in which to set off?