Looking for something to think about next time you gaze at your reflection when brushing your teeth? Then Sara Santos has some mathematical inspiration for your next daydream in her MMP public lecture, Through the looking glass... again and again!. If Alice took a magic trip inside a conic arrangement of mirrors, what would she find in this mathematical wonderland? You can take a look through a 3D kaleidoscope to see what happens to Alice's cubes and icosahedrons!

Sara Santos is Clothworkers' Fellow in mathematics at The Royal Institution of Great Britain (Ri) and is responsible for coordinating the UK-wide network of secondary Ri mathematics masterclasses. Sara will be speaking at 11am on Thursday 11 June 2009, at the Centre for Mathematical Sciences, Cambridge, just down the hall from Plus! Admission to the lecture is free but by ticket only — for tickets please contact Kerstin Enright, Millennium Mathematics Project, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (01223 766839) or email: mmptalks@hermes.cam.ac.uk. You can also sign up for notifications of future MMP events at the MMP site.

And don't forget you can also see the London Mathematical Society's popular lectures on Monday 22 June in London and Tuesday 15 September in Birmingham. Come and see how physicists helped answer a hundred year old question about prime numbers and how random matrices and Riemann zeroes feature in a major Hollywood movie with Nina Smith. And Mark Miodownik will explain how fleas can jump over 100 times their own height, flies can walk on water and a hamster can survive falling from aircraft without a parachute.

Admission is free, but by ticket only. For more information and tickets, contact Lee-Anne Parker, London Mathematical Society, De Morgan House, 57-58 Russell Square, London,WC1B 4HS (email: leeanne.parker@lms.ac.uk), or visit the LMS website.

But if you can't wait til then, you can take a trip through the looking glass and discover the importance of scale to weightlifters and kitten on Plus!