Archive for the ‘Senior School’ Category

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Maths News: Volcano Survivor 2

May 8, 2018

Kilauea erupts in Hawaii MAY 2018.

The amazing maths of volcano eruptions.

Once lava flows are established new RIVERLETS can run on top of the original lava flow at great speed.
Puu-Oo-USGS lava riverlets

The fastest Lava flows recorded were in Hawaii in 1950 when Mauna Loa erupted. The lava traveled at 6 miles (10 kilometers) per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 60 miles/hour (97 kph)

Can you out run a lava flow?

You are 2 km from the volcano rim and start running.

VL =   97 kph = 1.6 km per minute (k/min)

     =   60 mph

VH = 18 kph = 0.3 km/min

   = 11.2 mph (miles per hr )

GRAPH:

How long will it take for the lava to catch you?

Mauna Loa Volcano Lava Flow 1950 2

 

SIMULTANEOUS EQNS:

How long will it take for the lava to catch you?

Mathspig simultaneous Eqn 2

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Maths News: Volcano Survivor 3

May 7, 2018

Kilauea erupts in Hawaii MAY 2018.

The amazing maths of volcano eruptions.

One of the greatest dangers in a volcano eruption is not the lava flow OR being hit by a lump of flying lava or rock, but by being choked by the fast moving scorching hot pyroclastic cloud.

Mt Unzen volcano-world

In 1991 pyroclastic cloud blew out of the side of Mount Unzen in Japan. NASA has an excellent diagrams for such an event here.

According to the NASA website:

Highly mobile, these flows reach velocities of up to 400 kilometers (250 miles) per hour and can spread as far as 100 kilometers (60 miles) from the eruption point.

Can you out run a pyroclastic cloud?

Mathspig simultaneous eqn 3

Here is what happened in 1991 when the pyroclastic cloud blew out of the side of Mount Unzen in Japan.

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And the Oscar for Best Mathematical Performance Goes to …..

March 5, 2018

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And the Oscar for Best Mathematical Performance Goes to …..

Ben Zauzmer

Ben Zauzmer, a Harvard Applied Math graduate who has a 75 per cent success rate in predicting the winners of Oscar Awards every year, has correctly predicted 20 of 21 winners in 2018 Oscars, which is a success rate of 95%. 

How does he do it? He gathers thousands of data points on Oscar ceremonies over the past two decades – such as categories movies are nominated in, other award results, and aggregate critic scores – and he uses statistics to calculate how good a predictor each of those metrics is in each Oscar category. Then, he plugs in the numbers and that gives him the % chance that each film will win in each category according to  the Boston Globe.

Ben, who writes for The Hollywood Reporter, uses his mathematical model to produce  Bar Graphs like this:

This year the Best Picture was a close call, but Ben’s Mathematical Prediciton was correct.  

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Winter Olympics: Why do figure skaters spin so fast?

February 15, 2018

Here is the sensational pairs team from the 2018 Winter Olympics.

But why do ice skaters spin so fast?

Here is the math!

REASON  1:

Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.

L = mvr

L = angular momentum

v = linear velocity

r = separation of object

Louisa Barama, USA

Louisa Barama, USA

Let’s have a look at this equation:

Figure skate maths1

The fastest spin on ice skates was achieved by Natalia Kanounnikova (Russia) with a maximum rotational velocity of 308 RPM (rotations per minute) at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. See Guinness Book of Records.

 Record spin :  vr = 308 RPM

Other spins include:

Mao Asada, Japan, triple Axel

Mao Asada, Japan, triple Axel

Triple Axel spin vr = 220 – 280 RPM

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 Maximum Triple Axel spin vr = 402 RPM

Skaters can spin faster during a triple axel jump because there is no friction from the ice slowing their spin.

To complete a quad axel, it’s estimated that the skater would have to rotate in the air at:

540 rpm.

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Camel spin vr = 90 RPM

More info here.

Kim Yuna, South Korea

Kim Yuna, South Korea

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REASON 2:

How can a figure skater move from

a camel spin into a very fast standing spin?

Now, mathspiggies, you must separate Linear Velocity (v1 ) from Angular Velocity (vr ). Linear Velocity is measured in m/sec ie. it is the speed of, say, a skaters foot around the circle. Angular Velocity is measured in either RPM (Revolutions Per Minute) or degrees or Radians per minute. Ie. It is the rate of spin. We can’t judge how many m/sec a skaters foot is moving in a circle. We can only see how fast they spin. In other words, we see their Angular Velocity. When a skaters foot is in the Camel position that foot travels in a very big circle.

But when that same foot is in a Triple Axel postion it moves in a very, very small circle.

Patrick Chan, Canada, Camel Spin

Patrick Chan, Canada, Camel Spin

Patrick Chan, Canada, Triple Axel

Patrick Chan, Canada, Triple Axel

figure skate maths 2

By halving the radius, firstly, a skater’s Linear Velocity doubles due to the conservation of angular momentum.

Then, secondly, by halving the radius the circumference of the circle moved by , say, the skaters foot is halved.

Overall, by doubling the velocity around the circle and halving the circumference a skater increases their rotational velocity by a factor of 4.

Look at the numbers:

Camel spin vr = 90 RPM

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Triple Axel spin vr = 4 x 90 RPM = 360 RPM

That’s about right.

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5. It’s Too Hard

September 29, 2017

The Complaint:  

It’s too hard!………………

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The Cause:

This response often results when students face some new topic – often beyond numbers – that students can’t handle on auto pilot. Instead of working through the problem, they crash and burn.

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The Solution: 

I’m going to tell you a story. Bear with me for a minute. You did maths from Grade 1 to 6. You’re cool. No major dramas. Then something happens. A new topic, perhaps. Or a new teacher and a new topic. You don’t get it. You sit there looking confused. And then you do this. You say ‘I can’t do maths’( See post here) or ‘It’s too hard’.

In my maths teacher days terror topics were:

Long division

Algebra

Dividing Fractions

Geometry (because so few students listen to what the teacher is saying.)

Trigonometry (Lot of, you know, things to learn. Equations and stuff.)

So you stop doing maths. You retire at the age of, maybe, 13 years.

If you hit the MATHS WALL, here’s what you have to do. Back up a bit. Do some warm up maths on the topic. It’s out there.

eg. The Kahn Academy. I’m not saying it is easy. (See THE MATHS SPEECH here) I’m telling you it is doable. Practise.

Maths is always TOO HARD when you give up. But when you try amazing things can happen.

Besides, if a raccoon can do it.

Here is an exercise that you didn’t think you could do. But it is entirley doable by Middle School students with patience.

Karate Maths of OUCH! That hurts!


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Pi in the Movies

March 8, 2017

Pi Day … 14th March ….. 3.14

Pi Day celebrates an AMERICAN Pi because:

1. AUSTRALIA and UK:

Australia and UK write their dates DD/MM/YY and the 14th March or 14.3 is nothing to get excited about.

2. EUROPE

Pi in Europe is pronounced Pee. So 14th March Would be

Pee Day.

And Pee Day would not be something to encourage in Middle School. Also the perfume below is hilarious in Europe.

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Nevertheless, here are 2 interesting appearances by Pi in the movies plus a middle school challenge to count the Pi’s in the movie clip.

1. A Beautiful Mind

In this movie where Russell Crowe plays Mathematician Nobel Laureate John Nash, there is a maths  blooper involving Pi. Watch for pi on the window at 43 seconds.

You should have seen 0<π<1. But we all know π = 3.1415 etc.  For those mathematically fastidious an argument can be put that π can be used as a variable, which would make the statement true. But π is a universal constant so using π as a variable is just STUPID.

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2. Pi: The Movie

This 1998 psychological thriller promo clip is also the coolest maths promo you will ever see. It is only 1.42 mins long and it is big on π. But be warned the full lenght moive (SPOILER ALERT) involves madness, π and self-lobotomising with a power drill with a ‘happy’ ending.

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Pi Day Challenge:

How many times do you see π in this clip? Watch carefully!!!!!

 

 

 

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Pi on TV

March 8, 2017

1.  The Simpsons

When Marge is accused of stealing from Apu’s Quickie Mart his memory is tested. He says his memory is very good. He can recite pi to 40,000 places!!! Also on Numberphile: A Mile of Pi.

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2.  The Late Show with David Letterman

Maths savant Daniel Tammet explains that he can recite Pi to 22,000 places. But wait until you hear how long it takes. Amaaaazing!!!!!

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3.  Star Trek

Spock sorts out a computer with the command to calculate Pi. Cool!!!!

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4.  Mathletics

Look for the second maths blooper in this clip. The folks at Mathletics get Pi wrong!!!!! Great spotting Mathologer.

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5.  MTV Kate Bush

Some may prefer to listen to Apu reciting Pi to 40,000 decimal places. Nevertheless, here is Kate Bush singing about Pi.