Finding Nemo: Try Algebra

The Hunger Games Maths

The Hunger Games is about MATHS. Here are some interesting Hunger Game statistics.

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THE PLOT:

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In Suzanne Collin’s book, The Hunger Games, 12 districts in the land of Panem are suppressed and controlled by a vicious elite, who dress like neon-coloured French courtesans.

Each year the cruel rulers select one teen of each sex between the ages of 12 and 18 from each district to become tributes, who must fight to the death in a televised, sponsor-supported media event called The Hunger Games, set in a staged wilderness.

Only one tribute can survive. Katniss Everdeen and Peeta Mellark from the poor coal-mining District 12 are the local tributes for that year and must play at being star-crossed lovers to gain sponsor support and survive.

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THE MATHS:

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……………………………………………….……..The Reaping…..

Tributes are selected in a process called The Reaping. The names of the, approximately, 2,000 young people in each district are placed in separate barrels for males and females and the names are drawn out of these barrels BUT…

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12 year olds …….. 1 slip

13 year olds ……..  2 slips

14 year olds ……..  3 slips

15 year olds ……..  4 slips

16 year olds …….. 5 slips

17 year olds ……..  6 slips

18 year olds …….. 7 slips

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BUT you can gain extra ‘food’ if you accept for more name slips.

Gale Hawthorne (pictured above), Katnis’ friend from District 12, has 42 slips in the barrel. What are his chances?

We will assume that there are 1,000 teens of each sex in each district and an equal distribution – rounded off – for each age group to 1000/7 = 143

 

 

Age Group	Name slips	Total Name Slips	Probability of being REAPED	Probability P
12	1	143	1 : 4004	1: 4004
13	2	286	2 : 4004	1 : 2002
14	3	429	3 : 4004	1 : 1335
15	4	527	4 : 4004	1: 1001
16	5	715	5 : 4004	1 : 801
17	6	858	6 : 4004	1 : 667
18	7	1001	7 : 4004	1 : 572
total		4004

 

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Hunger Game: Survival Maths 1

How long can you live if you are bleeding?

Unlike Kill Bill where Tarantino used, literally, hundreds of litres of fake blood (See Mathspig Post: Don’t Bleed Your Fake Blood on Me), The Hunger Games shows very little blood.

Nevertheless 11 tributes are killed violently in the first few minutes of the game and Peeta is wounded later in the movie(pic with Katniss above).

To calculate how long you would last in The Hunger Games if bleeding we must know your volume of blood and the rate of bleeding.

1. How much blood do you have?

According to the BJA, the British Journal of Anaesthesia, blood volume is  7% of body weight in adults and 8 – 9 % of body weight in children.  Doctors are not confusing weight and volume. Blood is very close to the density of water and so 1 litre of blood weighs 1 kg. 

(NB: Future Engineers: Blood does not flow like water as the blood platelets affect the viscosity.)

Using blood volume (in litres) as 8% of body weight (in kg) then typical blood volumes for teenagers would be:

Age Group	Blood Volume litres Female	Blood Volume litres Male
12	4.3	4.0
14	4.7	5.1
16	5.0	6.1
18	5.3	6.6

 

2. How long would you last if bleeding?

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Obviously, it will depend on the rate of bleeding.

According to the BJA massive blood loss equals a blood loss rate of 150ml/min or 50% of blood volume loss within 3 hrs.

 BLOOD LOSS EQUATION:

B = total blood loss ml

R = rate blood loss in ml/ min = 150 ml / min

t = time min

B = Rt

B = 150 t

According to New Scientist loss of blood IN THE AVERAGE ADULT produces the following symptoms:

A  750 ml: feel blood loss

B  1500: weak, thirsty & anxious

C  2000 ml : dizzy, unconscious

D  3000 ml: Dead

See A, B, C and D on graph below.

3. How long have you got?

First, calculate  50% of your blood volume for your age.

Now go to the blood loss graph and see how long it would take you to lose this volume.

You can stop doing the maths now, mathspiggies, and get some help to stop the bleeding.

Hunger Games : Survival Maths 2

Katniss’ weapon of choice is the bow and arrow.

Mathspig noticed in the film that Katniss was aiming the arrow directly at the target. This is a problem. Arrows drop under gravity. If Katniss aims directly at the target she will hit it below her aim point. To overcome this she must raise her arrow aim.

What angle should she choose?

Robin Hood used a long bow and in the film Robin Hood archers raised their bows at a very high angle to cover long distances. See the diagrams below from Robin Hood Give Us Your Best Shot

 

 

 According to The Flaming Arrow the speed of a modern arrow is 100 m/sec with a 65 lb draw weight.

Mathspig believes in using the SIMPLEST maths solution. In this case, very short arrow flight times are involved. 

So we will assume the arrow velocity (V_a) equals horizontal vector speed (V_x). This is an approximation that makes the maths sweet. Such an approximation might work for the arow flight in the first diagram (above), but not in the second.

First, mathspigs, we’ll calculate the arrow flight time to a target 100m away and then we will calculate the distance the arrow would drop vertically in that time as this will tell us the point in the air where Katniss should aim.

 NB: An arrow will drop 4.9m over 100m to the target. In other words, Katniss would miss a human completely if she did not allow for gravity. Experienced archers automatically make this adjustment to their aim.

Gravity Eqn in the graph above comes from School for Champions

Harry Potter Needs Maths

What has Harry Potter to do with Maths?

Watch this video of Harry Potter and the Half Blood Prince: Death Eater Attack.

You can click on the link here or below (Video will only play on You Tube site):

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A recent article in The Guardian, UK, explained the link between Harry Potter and Maths:

‘(Alex)Hope, managing director of the visual effects firm Double Negative said: “In Harry Potter [and the Half Blood Prince], the opening sequence has Death Eaters flying across the river Thames, destroying the (Millennium) Bridge between St Paul’s and the Tate Modern.’

“The way you create that is people who understand computational fluid dynamics, they know how water moves. They take the physics that’s used in modelling rivers and the flow of water and apply that in our world. People doing it need an artistic sensibility as well. An understanding of maths and science is fundamental to many of the disciplines in our industry.”

Fluid Dynamics is the study of fluid flow. You can look at this picture (below) and see the similarity to the Death Eaters water-flowy appearance.

Here is a experiment showing lamina Vs turbulent flow in water. Mathspig did experiments like this at university in Chemical Engineering. Equations can be scary, mathspigs, but not necessarily.

Here is a water flow equation for a sharp edged weir with a V notch out let from AQUATEXT:

Q = 0.266 x cB x (2g)^0.5 x H^1.5

where;

Q = water flow rate, m³/sec

B = width of the weir at the flowing rate

c = discharge coefficient, average 0.62

g = gravitational constant, 9.81

H = Height of the water over the weir, measured behind the weir edge, m

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Here is a real flood caused when water was released from a real weir or dam.

In 2011 operators of the Wivenhoe Dam in Queensland (above) had to release water to stop the dam collapsing during severe floods.  8,000 properties were flooded.

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More @ News Limited 

Combine the flow maths for a weir (equation above) with computer graphics and you have a realistic flood film sequence!!!!!!

Or maybe a really unrealistic but terrrrrrrrifying sequence:

Aghhhhhhhhhh!!! We’re all gonna die or …. like …

have a really amazing white water raft ride, maths dudes!!!!!!!

Ball Park Figures or Brad Pitt Does Maths

MONEYBALL is a film starring Brad Pitt and  Philip Seymour Hoffman and Jonah HIll on current release in Australia. It is based on the true story of Oakland A’s Baseball team manager, Billy Beane (Pitt), who along with Ivy League Economics graduate and Uber Maths Nerd Peter Brand (Hill) used player stats to save the Oakland A’s baseball team in 2002. 

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Not only does Billy Beane have to deal with enormous budget restraints ( Oakland A’s budget was $4o million compared with the Yankee’s $125 million), he showed that the statistics were more effective than experience ie. the  stats BEAT the club selector’s know-how.

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Mathspig, who played softball in Australia – bigger ball, similar rules – saw the film and lerved the maths. Basically, Billy Beane bought up players with one particular skill – holding first base, stealing bases and the like – thus boosting the overall stats for the team. But Mathspig found some of the calculations weird.

This equation is called the Pythagorean Expectation. The wha? Mathspig is sooooo confused.

WHAT’S GOING ON?

Mathpig went searching for an expert opinion and found it at MATHS GOES POP, an awesome blog linking maths with pop culture and written by a mathematics PhD student at UCLA.

Mathspig won’t give a spoiler for the film, but found the maths is BASEBALL MATHS. It’s a formula used for baseball only and named after Pythagoras because it sorta looks – chew gum here and try a Brad Pitt drawl- like the Theorem of that Greek Math Guy. You do not need to use this EQUATION unless, perhaps, you are going to coach the New York Yankees.

Even IF YOU DO COACH THE NEW YORK YANKEES this equation, doesn’t give you that much information.  We will fix ‘runs allowed’. OK. If ‘runs scored’ is high Win is high; it ‘runs scored’ is low Win is low. Um, this means SCORING RUNS is GOOD. Yeah! We knew that without the maths.

If you are interested in the maths, have a look at MONEYBALL MATH on the Math Goes Pop blog otherwise just keep eating your popcorn and enjoy the film.

WHY JUDE LAW CAN’T DO MATHS

It’s not often that we have British actor Jude Law ( above) explaining maths to us, but in the new Hollywood film CONTAGION

he demonstrates how quickly a deadly virus could spread … (1.17 point on trailer)

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Jude Law plays the colourful blogger Alan Krumwiede. Gwyneth Paltrow’s character dies and Matt Damon tries to save his daughter. (See pics)

   

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Krumwiede says ‘ On day one there were 2 people, then 4, then 16 … in three months it’s a billion. That’s where we’re heading.’ Is he right?

LETS CHECK IT OUT MATHSPIGS

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.Now this bug is highly contagious, but Krumweide’s estimates start high and end low. In the film he says the number of infected people will grow according to the series 2, 4, 16, 256 and then a number Mathspig,um, missed. (I was munching popcorn.)

This is wrong. According to this progression by Day 3 each person must go out an infect 16 other people. By Day 4 they must infect 256 people each. By Day 5 they must infect 65,536 people each. That is a BIG cough.

Then he claims that in 3 months or 90 days 1 billion people will be infected. That’s so sweet. If the Gweny bug was so highly  contagious the human race wouldn’t last that long. Oddly, however, this number has synergy with the TWILIGHT VAMPIRES.

Even if each germ-riddled person infected only 1 other healthy person each day, this is how long we would last:

You may need to use the WEB 2.0 calculator to solve this problem.

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Not everyone on earth would die, of course. As the numbers drop so do the infection rates. Meanwhile, some people in remote areas would not get infected and some people would have immunity and that’s when the plot gets hot, HOT, HOT!!

Top 10 Funny Maths Videos

James Blunt : Love Triangle

That’s Mathematics  Song plus Maths Mistakes Galore!!!

Mad TV Funny Maths video

Tom Lehrer:  New Maths

Fab I will derive Song

Weird but funny!

I am Algebra

How to AVOID the Top Ten Algebra Mistakes

by Following these Top Ten Algebra Rules

Black Adder Addition

Fractions to Beatles Song

And now for our Celebrity Top of the Pops:

Simba Sings a Maths Song

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

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.

Make me feel real loose like a long legged goose!!!

Everyone knows that women’s magazine editors digitally alter photographs of models that appear in their mags. When I finally did the maths I was shocked.  See: Odd Bods in Marie Claire

This model had legs 89% longer than a standard size 12 model in the same edition of the magazine and with the same waist to hip measurement! Looking at this model made the standard size 12 model look like a dumpy little garden gnome. Looking at these images distorts our view of normal body sizes or anything close to it.

Models can be given the appearance of long legs by the angle of the camera (Looking up at the model on the catwalk, for instance), by wearing extra high stiletto heels and/or by wearing bathing costumes with high cut legs. Then photo editors use photoshop to stretch their legs.

While pictures of male models may be digitally altered to remove skin blemishes, body hair and add abs, it seems to me that their legs are not digitally stretched and certainly not by 89%! But we have this 89% number now and we should use it.

So Mathspigs here are some male celebrities with a standard pic and then with their legs – from the hip down – stretched by 89%.

This was very simple maths. I used photoshop to edit the pictures and set their legs at a 189% vertical stretch. 

Check the maths:

Standard leg length = 100%

Vertical Stretch        = 89%

FINAL LEG LENGTH  = 189% 

Look at these pics and you decide if they look OK or ridiculous. I cannot decide for you. But I have thrown in the pics of the horse and the giraffe just to show how the practise of digitally stretching models images distorts reality. 

Here we go mathspigs. Lets play STRETCH LIMBO!!!!!!!!!!!!!!!!!!!!!!!!!!

Zac Efron

Maybe these

long legs would

help his

dancing, but…..  if he did the splits he’d never get up again.

Robert Pattison

plays

Edward Cullen

in the Twilight series. See TWILIGHT MATHS II

Edward is an ethical vampire

at this height he’d have to chase giraffes.

Justin Beiber

As my photoshop leg stretching skills improved

I found that

our eye begins to accept legs stretched

from the top of the thigh but not higher up the body.

Check out these stretch-horses.

Both images have legs stretched by

89% but the second horse has been stretched from the mid-body point down. Now look at the normal horse. It looks like it has SHORT legs!!!!!!! These images have distorted our sense of reality.

Here are some sports stars.

Sam Gilbert plays Aussie Rules football 

for ST KILDA.

PS: Mathspigs dad and two Uncles played for St Kilda.

My Dad broke his leg when he ran into the goal post. 

They sent him off to hospital using the local bus!!

This was along time ago.

My dad

and

two uncles

are in the

St Kilda team

photo 

together

in

1946.

Heath Grundy 

plays 

Aussie Rules 

Football 

for 

the 

Sydney Swans.

 

 Usain Bolt

 We would like to believe that Usain Bolt has long,

long legs.

 However he doesn’t need legs as long as the stretch photo suggest.

He is already the world’s fastest runner.

 

  The giraffe looks quite reasonable with extra long legs.

 Then again you could argue that

the real giraffe shape

is weird.

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Now for a few rock stars.

 This is Vampire Weekend.

 The long Weekend is  Left.

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Here is CUT OFF YOUR HANDS. 

Cut Off your Hands UNCUT is Right.

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 This is the rock group GRIZZLY BEAR.

Look at the way our eye works.

Look at the guy in the shorts. His leg has been extended from the knee down. Looks wrong.

The guy in the black pants legs look OK even though extended 89%.

The guy squatting is totally distorted as his whole body and head have been stretched.

 Now you’ve seen a horse, a giraffe and a grizzly bear. 

Finally, a bit of fun.

Here are some fictional characters. 

Harry who???? The batman toy looks appears in proportion mainly because action figure toys are usually made with short muscly legs.

 

  - I used the standard 89% stretch here. I was hoping to give Spiderman legs like a spider.