Archive for the ‘Senior School’ Category


Isaac Newton, The Great Plague and how he filled in his Time!

March 18, 2020

I am grateful to Jeff Jacoby and his column, Arguable, in the Boston Globe for reminding me of how Isaac Newton filled in his time when he went into self-isolation during The Great Plague of London in 1665-1666.

He spent time thinking and the results were astounding!!!!!



The Equation that tried to break the internet!!!

August 3, 2019

The following equation went viral on Twitter like the Yanni & Laurel sound Tweet. What answer do you get?

The Equation that tried to stump the internet! New York Times


VAMPIRES: a math horror story

March 6, 2019

You will find TWILIGHT TV series Math here.


Math Nerd Love

February 14, 2019

The New York Times (The Perfect Valentine? A math formula 14 FEB 2019) has published an interactive widget from my favourite math website IMAGINARY for Valentine’s Day.

Here is the formula:


You’ll find IMAGINARY’S  interactive LOVE widget HERE.


What do the Sydney Opera House and Freddie Mercury have in common?

November 6, 2018

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.


I Can’t Sleep: Caffeine Math Part 3 USA UNITS

August 14, 2018

I Can’t Sleep Math: Caffeine Maths METRIC 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.

Caffeine content sources Caffeine Content Data Base

Street art by JEKS, South Carolina

The Half life equation is an exponential function.

The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;

10 black teas

7 instant coffees

4 cappuccinos

2 dark roast brewed

less than one cup of Black Insomnia Coffee.

Approx half this amount of caffeine for 14 yos.


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 )


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

Mauna Loa Volcano Lava Flow 1950 2



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

Mathspig simultaneous Eqn 2


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.


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

March 5, 2018


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.  


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!


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


 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.


Camel spin vr = 90 RPM

More info here.

Kim Yuna, South Korea

Kim Yuna, South Korea



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


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

That’s about right.