Freddie Mercury is back in the news with the release of the new biopic BOHEMIAN RHAPSOSDY. ( Mathspig gives it ⭐⭐⭐⭐⭐. But I’m a Freddie fan. ) So Freddie and the Opera House? What do they have in common?

NOTE: Uncanny likeness of biopic actors to the real Queen!

According to intmath The Sydney Opera House is a very unusual design based on slices out of a ball. Many differential equations (one type of integration) were solved in the design of this building.

You will never see a better parody of Queen’s ICONIC song BOHEMIAN RHAPSODY than Calculus Rhapsody By Phil Kirk & Mike Gospel (below).

And if you need to be reminded of the maths you will find links to texts here.

Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.

Once lava flows are established new RIVERLETS can run on top of the original lava flow at great speed.

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.

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.

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?

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

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 theBoston Globe.

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

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

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

Let’s have a look at this equation:

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 : v_{r} = 308 RPM

Other spins include:

Mao Asada, Japan, triple Axel

Triple Axel spin v_{r} = 220 – 280 RPM

……………………………………………………………………………………………..

Maximum Triple Axel spin v_{r} = 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:

Now, mathspiggies, you must separate Linear Velocity (v_{1} ) from Angular Velocity (v_{r} ). 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, Triple Axel

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.

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.

………………………………………………………………………….

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.