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Math in and out of the zoo Chris Budd

Math in and out of the zoo Chris Budd. Where does a mathematician go to find some maths when they are not in their office?. At play?. At Work?. Hyperboloid of revolution. About town?. By the beach?.

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Math in and out of the zoo Chris Budd

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  1. Math in and out of the zoo Chris Budd

  2. Where does a mathematician go to find some maths when they are not in their office? At play?

  3. At Work? Hyperboloid of revolution

  4. About town?

  5. By the beach? Chevron folding caused by the geometry forced by the interaction of rock layersmath can find the angle Singularities in rock folding described by the Swallow tail catastrophe:

  6. Folded rocks have unlimited possible shapes!

  7. Or maybe a trip to the Zoo? 3 5 1 2 1

  8. Some math problems from the zoo: Fish, penguins, flocks, crowds, bees, and the gift shop …. Bristol Zoo

  9. Math guide to mostCanadian animals

  10. 1. Fish:Artis Zoo Amsterdam, and hot fish

  11. T: Temperature of the fish Sa: Outside air temperature I: Inside air temperature Sg: Outside ground temperature V: Fan velocity Heat gained = heat lost Cooling due to fan Heat lost to air inside Heat gained by solar radiation Heat lost to ground

  12. Solve the formula to give the fish temperature T T Air temperature: Sa Fan velocity: V

  13. Hitting the press! =

  14. 2. Penguins at….

  15. Preservation of rare bird species requires them to be bred in captivity One way is to incubate eggs artificially • Need to control • Temperature • Humidity • Turning of the egg Very sensitive to the turning strategy! Eggs are turned by mother every 20 minutes

  16. Questions ….. Why do birds turn their eggs? Can mathematics help us to optimise the turning strategy and save the penguins at ..

  17. Blastoderm of lower density • Yolk is free to rotate

  18. Some possible reasons for turning eggs …. • Conduction of heat … this is what the zoo believes! • Dispersal of nutrients • Removal of baby penguin poo

  19. Modelling theconduction of the heat Q. Is turning needed to maintain an even temperature? Radius of egg R = 2cm Temperature = T Thermal diffusivity k = Heat equation

  20. 10 seconds 2 minutes 20 minutes Too short!!! Consistent with results from incubator

  21. In fact … turning is actually needed to move the nutrients and remove the waste matter Monitor the turning using an artificial nylon egg … And then reproduce this in the incubator

  22. 3.Birds of a feather flock together Birds flock, fish shoal and people crowd

  23. Each bird interacts with its nearest neighbours but the flock behaves like a single organism. Math describes this through equations for: alignment, vision,avoidance,intent

  24. People behave similarly in crowds but have attitude

  25. Idea: Individual in crowd is acted on by several forces • Global force: Intentions of the individual • Repulsive force .. Avoidance strategy • of people or obstacles : • Cohesive force of families and groups Put these forces together to work out the crowd behaviour

  26. Mathematical formulae for these [Helbing] Global force: intent Intended direction Local force: avoidance

  27. Scramble crossing

  28. Escape from the zoo!

  29. 4: But where are the bees?

  30. X-ray CAT scan the beehive .. In real time

  31. First take your X-ray Source X-Ray Detector Object ρ : Distance of the X-Ray from a fixed point θ : Angle of the X-Ray from a fixed line Measure attenuation of X-Ray R(ρ, θ)

  32. REMARKABLE FACT If we can measure R(ρ, θ ) accurately for enough X-rays we can calculate the density f(x,y) of the object Mathematical theorem proved by Radon (1917) Knappe Kop?

  33. Radon’s formula: basic equations of Tomography Radon’s formula leads to a set of equations for f Problems … there are over 1 000 000 equations to solve, and the information must be incomplete for short radiation times

  34. HAEMOLYMPH VENTRICULUS 0.05mm Good news … can now solve these equations rapidly using advanced numerical methods and compressed sensing techniques. And .. can then monitor the honey bees in high detail, and in real time

  35. Or even in ancient times

  36. At last .. A trip to the gift shop Problem 5:What do you buy? Robert Lang

  37. Maths can help you make the perfect gift Crease patterns are worked out using mathematics and obey strict mathematical rules. Canadian Bull Moose Stag Beetle Eg. At any vertex the sum of all odd (even) angles is

  38. Can even use Origami to Trisect an Angle or double a cube!

  39. I hope that you liked your trip to the zoo Good maths really is everywhere!!!

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