Download presentation

Presentation is loading. Please wait.

Published byAngel Marsh Modified over 3 years ago

2
Math in and out of the zoo Chris Budd

3
Where does a mathematician go to find some maths when they are not in their office? At play?

4
At Work? Hyperboloid of revolution

5
About town?

6
By the beach? Singularities in rock folding described by the Swallow tail catastrophe: Chevron folding caused by the geometry forced by the interaction of rock layers math can find the angle

7
Folded rocks have unlimited possible shapes!

8
Or maybe a trip to the Zoo? 3 2 5 1 1

9
Some math problems from the zoo: Fish, penguins, flocks, crowds, bees, and the gift shop …. Bristol Zoo

10
Math guide to most Canadian animals

11
1. Fish: Artis Zoo Amsterdam, and hot fish

13
T: Temperature of the fish Sa: Outside air temperature I: Inside air temperature Sg: Outside ground temperature V: Fan velocity Heat gained by solar radiation Heat lost to air inside Heat lost to ground Cooling due to fan Heat gained = heat lost

14
Fan velocity: V Solve the formula to give the fish temperature T Air temperature: Sa T

15
Hitting the press! =

16
2. Penguins at….

17
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

18
Questions ….. Why do birds turn their eggs? Can mathematics help us to optimise the turning strategy and save the penguins at..

19
Blastoderm of lower density Yolk is free to rotate

20
Conduction of heat … this is what the zoo believes! Dispersal of nutrients Removal of baby penguin poo Some possible reasons for turning eggs ….

21
Modelling the conduction of the heat Radius of egg R = 2cm Temperature = T Thermal diffusivity k = Q. Is turning needed to maintain an even temperature? Heat equation

22
Too short!!! Consistent with results from incubator 20 minutes 2 minutes10 seconds

23
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

24
3. Birds of a feather flock together Birds flock, fish shoal and people crowd

25
Math describes this through equations for: alignment, vision, avoidance, intent Each bird interacts with its nearest neighbours but the flock behaves like a single organism.

26
People behave similarly in crowds but have attitude

27
Global force: Intentions of the individual Repulsive force.. Avoidance strategy of people or obstacles : Cohesive force of families and groups Idea: Individual in crowd is acted on by several forces Put these forces together to work out the crowd behaviour

28
Intended direction Global force: intent Local force: avoidance Mathematical formulae for these [Helbing]

29
Scramble crossing

30
Escape from the zoo!

31
4: But where are the bees?

32
X-ray CAT scan the beehive.. In real time

33
X-Ray 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 ) Source Detector First take your X-ray

34
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?

35
Radons formula: basic equations of Tomography Radons 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

36
VENTRICULUS HAEMOLYMPH 0.05mm And.. can then monitor the honey bees in high detail, and in real time Good news … can now solve these equations rapidly using advanced numerical methods and compressed sensing techniques.

37
Or even in ancient times

38
At last.. A trip to the gift shop Problem 5: What do you buy? Robert Lang

39
Canadian Bull MooseStag Beetle Crease patterns are worked out using mathematics and obey strict mathematical rules. Eg. At any vertex the sum of all odd (even) angles is Maths can help you make the perfect gift

40
Can even use Origami to Trisect an Angle or double a cube!

41
I hope that you liked your trip to the zoo Good maths really is everywhere!!!

Similar presentations

OK

The Gas Laws u Describe HOW gases behave. u Can be predicted by the theory. The Kinetic Theory u Amount of change can be calculated with mathematical.

The Gas Laws u Describe HOW gases behave. u Can be predicted by the theory. The Kinetic Theory u Amount of change can be calculated with mathematical.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on k-map simplification Reproductive system anatomy and physiology ppt on cells Ppt on computer languages types Ppt on power sharing in india download music Ppt online examination project in java Ppt on business entrepreneurship and management Ppt on natural disasters for class 9 Ppt on beer lambert law definition Ppt on programmable logic array application Ppt on holographic display technology