Archive for the ‘trigonometry’ Category


3. Find a Ghost Ship

October 14, 2013

The Ghost Ship, Orlova, disappeared on 4 FEB, 2013 while being towed off the coast of Canada and has not been seen since. The 1,500 tonne 110 passenger Russian vessel is drifting somewhere in the Atlantic Ocean. Missing, Richard Fisher, New Scientist, 5 Oct 2013

Orlova 2

The Lydbov ORLOVA in action. 

Orlova 3

The Lydbov ORLOVA as a Ghost Ship.

Despite 2 separate SOS broadcasts from Orlova life rafts in March,

it has not been found. These SOS signals are the last two ‘sightings’ shown on the map (below),

but an aerial search did not find the GHOST  SHIP.

Map from

Map from

The Problem:

Ghost ships, pirates and illegal fishing vessels do not want to be found. They do not give off radio signals or identify themselves in any way to other vessels. Ghosts ships, in particular, are dangerous because other ships can crash into them at night. Seven ghosts ships have been found since 2000 including an 80m tanker off the coast of Australia. 

GPS is not always accurate. (Scroll down to see error chart: 10. Design Cool Techno Stuff )

Ships must use radar to get instant readings of other vessels in the shipping lane. Can you find a GHOST SHIP Mathspiggies?

bae-radar used by BRitish Fleet



Radar, short for “Radio Detection And Ranging”, sends out short pulse microwave beams that either focus on a narrow area (eg. speed cameras) or scan an entire semi-circular dome (eg War ships). Radar measures the angle and time taken of the reflected echo. This gives the location and altitude (distance and angle) of the airplane or ship.

It is used to detect the location, speed and direction of weather fronts, cars, airplanes, ships and more.

The weather radar beam is typically reaches about 322km or 200 miles. Here is the current radar map produced by the Bureau of Meteorology at the Terry Hills unit north of Sydney (pictured below)


BOM radar 1  sydneyBureau of Met RADAR with protective dome

Bureau of Met RADAR
with protective dome


The Doppler Effect is used to calculate the speed of the ship. Every kid knows the Doppler Effect. eg.  sound of a racing car turning a corner. High pitch approaching, low pitch leaving as sound waves are shorted on approach and lengthened on departure. Today Doppler Radar is automated. This was not possible before computers. eg. World War 2

The Maths:

You are going to do some World War II Radar Operator maths.

To do RADAR MATHS you must THINK HARD and picture what is happening in your mind. All you see on the screen at any one time is YOUR SHIP’S POSITION (in the middle) and a BLIP showing the GHOST SHIP’S POSTION as the microwave beam scans the ocean.

You mark the GHOST SHIP POSITION on screen  and then do these calculations. But remember this …every time you see a blip you have moved too.

Radar Maths 1

 Radar Maths 2

Now we’re going to look at the sort of calculation needed if ships we’re heading on a collision course. You will find all the GHOST SHIP DATA under the RADAR screen (below).

RAdar Maths 3


10. Way Weird Maths

January 15, 2013

In the Way Weird Maths department are:

1. The Back Hair Coiff

 back hair number

2. The Fibonacci Hair Flip

 fibonacci hair flip


Fibonacci Hair

fibonacci hair

3. Fractal Jewellery

This jewellery made with diamonds and sapphires by Mark Newson for the jeweller Boucheron is based on the Julia Set shown below.

fractal jewllery by Mark Newson for boucheron…………………….

fractals Julia setJulia Set


4. Scary Math

Halloween or not, this guy is scary!!!!!

halloween geek

Could this be the math teacher you do not want to meet int he dark?


6. Geometric Hair

Mathspig calls this the Isosceles coiff (below). You have to see it from the Right Angle!!!

 geometric hair 2

The Cubic Hair. The model is actually saying ‘Geometry stole my brain’.

geometric hair 3 

The Tesselation tresses. The hard work is is walking into the wind so you don’t upset the tessellations.

geometric hair 4

7. Maths bling watch

Hammacher Schlemmer is offering The LED Matrix Watch for $79.9

How do you tell the time? Work it out mathspigs.

math bling watch 2.aspx

8. Maths is Evil Mug

See, maths is evil. We have the proof!!!

weird mug

9. Math Body Art

These are scary maths tatts. What if the tattooist failed maths? He might make a big mistake.  And you’d have maths teachers forever correcting your back … possibly with red pens.

 math knuckle tattoo….You wanna punch in the face by an inverse function

math tatt 2

………… I am the unit circle of an exponential cult!!!

math tattoo

…… I am a standard deviation or is that a deviant?

10. Truly scary math tatt.

Someone this crazy about math may not be stable.

 weird math 1

… I am the Math Murderer of your worst nightmares. (Cue: hysterical laugh.)


Weird Math Activity

Here is the challenge. Can your maths students make up clock faces (they need not be round) that tell the time using only:

1. triangles

2. algebra

3. matrices

4. fractions

5. a bar graph

6. a line graph

7. pi

8. trigonometry


The Trigonometry of the Fake Tan

May 4, 2012


Zombie Maths 5: Trigonometry

December 13, 2011

Zombies are dumb.

A Zombie starts walking toward your house from 10 km away.

He walks in a straight line, but he is 5 degrees off target.

How far away from your house will he end up away from your house?




The High -pot-in-use!

Everyone must know the HIGH-POT-IN-USE!


12 minute Maths Guru

July 4, 2011

Meet Salman Khan. He has put free maths on-line.

This article on Salman appeared in The Sunday Times, UK, 12 JUN 2011.

Salman, 28, started putting tutes online for his 12-year-old niece, Nadia, and things grew. So far the Kahn Academy’s claim to fame are:

* Over 2,400 videos including hundreds and hundreds of 12-minute maths tutes

* Over 63,000,000 lessons delivered.

* Bill Gates kids use the site.

* A staff of 1 with funding from The Bill and Melinda Gates Foundation.

* Tutes on Biology, Chemistry and Physics too.

You can look up the maths tutes by topic @ The Khan Academy.

Or search topics on Youtube eg. Introduction to Conics Khan

Why Does Mathspig like The Kahn Academy? Because it’s:

1. Free.

2. Quick

3. Clear

4. Low-key







Salman gives digital chalk-and-talk tutes like a teacher. He hand draws the equations and graphs. He uses a calculator from time to time, but he tends not to use whizz bang spreadsheet graphs or perfectly presented textbook equations. It’s a bit wobbly and it’s all coming from Salman’s head.

And students like this approach. It makes maths look do-able.

Go, Salman.

Mathspig thinks you are just GORGEOUS!!!!!!!!!

 Australia’s Year 7 – 12 Maths Curriculum is already on-line and free, funded by McDonald’s. See What are maths teachers for, sir?

The tutes on Maths Online are produced by Aussie Maths teachers and they are very good. Mathspig, of course, imagined the quadratic function tutes might look something like this:


Robin Hood Give Us Your Best Shot!!!!!!!

May 30, 2010

Mathspig went along to see the movie, ROBIN HOOD, starring Russell Crowe and Cate Blanchett. I was interested in the film for several reasons.

Firstly, Cate Blanchett went to the same primary school as Mathspig’s children in Melbourne. Such is our Aussie egalitarian attitude to education we do not single out past students for special attention.  No picture of Cate Blanchett appeared at the school during Mathspig’s kids education and none, as far as I know, to date.

Secondly, I’m amused that two Australian stars featured in an American remake of a British classic tale. I was just a bit disappointed that Russell Crowe didn’t say something like ‘No worries, King John, mate!!!!

Another amusing aside was that the re-engineered history in this Ridley Scott tale meant Robin Hood had a great influence on British History. I am only too delighted to discover that Russell Crowe wrote the Magna Carta.

How Far Could Longbow Men shoot their Arrows?

I was very intrigued by how the long bowmen fired their arrows. Robin Hood begins the film as a long bowman called Robin Longstride. The film critic for the New Yorker suggested ‘Longstride’ was not the ideal name for Russell Crowe’s nuggetty Robin. I think Robin Chunky-Guy might be more appropriate.

When I did some research ( Longbow arrow speeds)I found that Russell Crowe’s build was closer to the original longbow men than earlier Robin Hoods such as the tall and rangy Errol Flynn (Shown).  It is believed that longbow men of the era could draw -a force (on the bow string) of 150 lb-f (pound force) or 667 N (Newton), which is, at least, twice the draw force of bowmen today who, if they are good, can draw 60 – 80 lb-f or 267 – 356 N.

Longbow men used heavy wooden arrows and not the carbon shafts used by archers today. Arrow speeds are estimated for the longbows to be up to 310 f/s (foot per sec) or 100 m/sec.

In the film I noticed that Robin Hood – especially in one dramatic shot at the end, – aimed his arrow at a high angle in the air. ( See Below)

Mathspig believes you should always find the easiest way to do any calculation. so here is the EASY way. Assuming there is no wind or wobbly arrow movement we can split the arrow velocity into its horizontal and vertical components (Using vectors. If you haven’t done vectors just go along with it.) Then interesting things happen!!!!!!!!


We haven’t allowed for air resistance in the flight of the arrow so it would slow down….. BUT Russell Crowe … I mean ROBIN HOOD was right.AIM HIGH and your arrows go a long, long way!!!!!!! Of course, the straight arrow traveling at 100 m/sec would travel 1000 m in 10 seconds or 1 km!!!!!! 

Mathspig finds this amazing.


Sharp Shooter Maths

May 14, 2010

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Mum fed the prisoners. Dad’s car an old FC Holden, maroon and white with a pink door, was the police car. And the police phone sat in the kitchen.

Australia has a very strict gun laws today. Thank goodness. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against the fridge in the kitchen – without it’s 6-bullet magazine – in case my dad was called out to some police emergency.

There were a number of gun incidents in my childhood. One time my mum was cleaning the house. She usually put paper rubbish in her apron pocket and threw it at the end of the day into our combustion (wood-fired) stove. She forgot she had three .22 bullets in her pocket. It took some time for the bulletsto heat up.

My parents were in bed when bullets started exploding in the kitchen. The explosion blew off the hot plate and blew the ash door open covering our kitchen in grey ash. And it nearly gave my dad a heart attack. This was a typical story of my childhood and why I became a humour writer.

My Dad the Sharp Shooter My dad stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more.

This math post has been updated here:

Sharp Shooter Math …. USA units

Medals, Meglomaniacs and Sharp Shooters…….. The Math USA units