**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.**

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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**.

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.

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)

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

**V _{L} = 97 kph = 1.6 km per minute (k/min)**

** = 60 mph**

**V _{H} = 18 kph = 0.3 km/min**

** = 11.2 mph (miles per hr )**

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.

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

**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. **

**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 = angular momentum

v = linear velocity

r = separation of object

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.

Other spins include:

……………………………………………………………………………………………..

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:

…………………………………………………………………………………

More info here.

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.

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:

…………………………………………………………………………………

That’s about right.