Ocean Mathematics

Ocean mathematics into slide
Image Copyright 2013 by Passy’s World of Mathematics

Welcome to Ocean Mathematics!

Passy’s World is pleased to present a series of lessons all about the Mathematics related to the following aspects of the World’s Oceans:

Mathematics of Ocean Waves

Mathematics of Surfing

Surfboard Design and Geometry

Power Generation from Waves

Mathematics of Tsunamis

Sharks Mathematics

Mathematics of Ships at Sea

These lessons have been assembled as part of a Lecture Presentation at the Mathematics Association of Victoria 2013 Annual Conference in Melbourne Australia.

Links to each of these lessons are given below, as well as a link to the PowerPoint Presentations which were used during the lecture.


Mathematics of Ocean Waves and Surfing

Surfing Mathematics 1
Copyright Image Purchased by Passy’s World from Dreamstime.com

In this lesson we look at some of the Mathematics associated with Surfing.

We cover the Mathematics of Ocean Waves, as well as the mathematics and physics associated with catching and riding a surfable wave. People do not need to think about mathematics when actually surfing; however there are certain mathematical realities which are foolish to ignore!

Click the following Link to access this lesson:

Mathematics of Ocean Waves and Surfing


Surfboard Design and Geometry

kelly slater doing big cutback
Image Source: http://wikimedia.org

This lesson covers Modern Surfboard Design, and its associated mathematical geometry.

First we look at the main types of Surfboards, and then we examine the specific geometries of the component parts. We also look at computerised shaping and manufacture of surfboards, involving 3D Printing technology and Parametric Geometrical Equations.

Click the following Link to access this lesson:

Surfboard Geometry and Design


Power Generation from Waves

Oceanlinx power plant in water
Image Source: http://2.bp.blogspot.com

In this lesson we look at Wave Energy from the Oceans, and some of the Mathematics and Geometry associated with this “Blue Energy”.

Click the following Link to access this lesson:

Wave Power Mathematics


Mathematics of Tsunamis

Tropical Tsunami
Image Source: http://millicentandcarlafran.files.wordpress.com

This lesson examines the Mathematics associated with the incredible destructive power of Tsunami Waves. It’s all about Equations and Algebra Substitution!

Click the following Link to access this lesson:



Sharks Mathematics

Shark Mathematics One
Image Copyright 2012 by Passy’s World of Mathematics

This lesson covers some mathematics associated with Sharks, such as Levy Walks, Biting Force, and Ratio and Proportion.

Click the following Link to access this lesson:



Mathematics of Ships at Sea

Blue Marlin Sinkable Ship
Image Source: http://i.imgur.com

This lesson contains some Mathematics of Ships including Archimedes Principle, Stabiliser Wings, the Plimsoll Line, the Bulbous Bow, and a number of other aspects relating to ship design and mathematics.

Click the following Link to access this lesson:

Mathematics of Ships at Sea


MAV Conference PowerPoints

To download the PowerPoint Presentations from the MAV Conference, click the links below and save the files to your computer.

Mathematics of Ocean Waves and Surfing

Click the link below to download this 12MB PPT File:



Surfboard Design and Geometry

Click the link below to download this 11MB PPT File:



Power Generation from Waves

Click the link below to download this 3MB PPT File:



Mathematics of Tsunamis

Click the link below to download this 2MB PPT File:



Sharks Mathematics

Click the link below to download this 2MB PPT File:



Mathematics of Ships at Sea

Click the link below to download this 4MB PPT File:



AMC Teacher Resources

AMC website Image

The Australian Maritime College has an excellent set of free resources for Mathematics Teachers.

Among these are some very good mathematical exercises related to Ocean Mathematics.

The AMC is planning to add more online interactive lessons, but as of late 2013 the current the interactive lessons are as follows:

A Study of Similar Vessels (an application of Curve Fitting) – 5mins

Wind Farm Feasibility Study (an application of Probability) – 12mins

Vessel Speeds in Waves (an application of Differentiation) – 5mins

Ship Hydrostatics (an application of Integration) – 12mins

Wave Refraction (an application of Trigonometry) – 12mins

Ocean Waves (an application of Superposition) – 5mins

Scaling Laws (an application of Algebra) – 8mins


Go to the following link to find their Resources page:


To get the workbooks and other resources, it is necessary to register your school and complete an order form online.

These resources are free to Australian schools, and if you would like to see what some of the workbook exercises look like, then check out the following link:

Click here for AMC Online Maths Workbook PDF


The AMC can be contacted about this program at the following email address: whystudymaths@amc.edu.au


Surf Aid Mathematics Resources

Surfing Mathematics 20
Image Screen Captured from Surf Aid Website

Surf Aid is a not for profit organisation sponsored by Billabong with a kean interest in the preservation of Mentawai in Indonesia.

The Mentawai Islands are a chain of about seventy islands and islets off the western coast of Sumatra in Indonesia.

It is totally free to join the “Surfaid Schools Program”, and all that is required is submission of your email address.

The Surfaid website can be found at this link:


Downloadable Free Units which are in ZIP and PDF format which could be of use to Mathematics Teachers are the following:

AUS Maths 12-14

Mathematics – Connections through Surfing


Destination Mentawai Islands

The Economics Of Aid

Crossing The Divide – Primary

These are all free PDF and ZIP file downloads

A Typical example might be the following questions about traveling to surfing locations on various Islands:

“If the motor launch can manage an average speed of 15knots, calculate the journey time between each
location. 1knot is 1 nautical mile per hour. You can assume there is sufficient sailing staff to keep moving 24h
per day. Round up your answers to the nearest day and complete worksheet 5.3.

If you move 10º around the equator how many nautical miles have you travelled?

What angle around the equator (change in longitude) corresponds to 1 nautical mile?”


Another activity we looked at was all about “Planning an Overseas Surfing Trip”.

Eg. Costs, Savings Plan, Items needed and their Cost, and so on.

It was very surfing orientated and might alienate non-surfers and female students, but could easily be adapted to be a group of friends planning a Bali Holiday, and undertaking various tours and activites whilst in Bali.

We will be going through all of the Surfaid Materials, and seeing what could be incorporated into some middle school mathematics, even though the school Passy works at has a tiny minority of students who have ever been Surfing.

We suggest you could easily do the same for your classes.



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