# Maritime Maths

 A Mathematics Talk given by Colin Wright Tagged As Talk Description
"Maritime Maths" introduces the audience to what was the major practical problem of the early 18th Century - safe navigation at sea.

Here is an outline of some of the aspects touched on:

• The tragedy on October 22nd, 1707
• Computing your position from bearings
• Using bearings from North
• Including error allowances
• Using relative bearings between multiple points
• Generalisation of Thales' Theorem
• Doesn't work over the horizon
• What shape is the Earth?
• Shadows during Lunar Eclipses show it's a sphere
• Eratosthenes of Cyrene measured the circumference of the Earth
• Summer Solstice (not necessary)
• Reflected in a deep well => Sun overhead - no shadow
• 7.2 degree shadow in Alexandria, some distance north
• Divide by 2*pi to get the Radius of the Earth
• Eratosthenes also invented Latitude and Longitude
• How far is the horizon?
• "Mountain" 5 metres high
• How far to get to that point?
• Uses Pythagoras - about 550BC
• Pythagoras of Samos - student of Thales
• Wouldn't accept Irrational Numbers
• Out of sight of land
• Measure Latitude with a Sextant or an Octant
• How does that work?
• Log / Knots
• 7 fathoms in 30 seconds = 5040ft/hour
• 47'3" in 28 seconds = 6075ft/hour
• How do we measure Longitude?
• That is the £6m question
• Prize offered in 1714 - 6 million pounds in today's money
• Many methods suggested
• wounded dogs
• Anchored ships with flares and cannons
• Measuring the Moon against a fixed star map
• Parallax
• Distance to the Moon?
• Acceleration due to gravity - value of g?
• Regular dropping - two ticks per second
• Pendulum timing
• Clocks
• Existing clocks were out by minutes per day
• Robert Hooke had a clock in the late 1600s
• Required sub-second error
• John Harrison, 1693-1776
• H1 - still can be seen in the Worshipful company of Clockmakers Guild Museum
• H4 - Met the requirement
• Never given the prize
• K1 carried by James Cook on his second and third voyages
• not on his first to Tahiti for the transit of Venus
• Galileo Galilei
• Acceleration is a time squared thingy
• Analysed the pendulum
• Or was that Isaac Newton?
• CPA / Closest Point Of Approach
• Intercept Problem
• Isaac Newton (1643-1727)
• Royal Mint / Royal Society
• Inverse square law of gravity
• Acceleration due to gravity
• Reflecting telescope
• GPS / Global Positioning System
• Speed of light
• 1638 Galileo Galilei
• Lanterns
• 1676 Ole Roemer
• Eclipses of moons of Jupiter
• Galilean Moons
• Stellar Aberration (1/200 degrees)

Other topics:
• Newtons Cannon
• Orbital Velocity
• Orbital Period