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**The following maths is suitable for Year 9+**

**but can be presented to lower grades just to show**

**maths is cool!**

Just another WordPress.com weblog

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**The following maths is suitable for Year 9+**

**but can be presented to lower grades just to show**

**maths is cool!**

Mona Chalabi is a** British-Iraqi data journalist** and illustrator based in London. She specialises in all things data.

An outstanding communicator her work proves that MATH can be artistic and ART can be data-based. She is an honorary fellow of the British Science Association.

Mona Chalabi Self Portrait **on INSTAGRAM**

**WARNING**: Mona Chalabi INSTAGRAM account is politically graphic and contains sexually explicit graphs. Yeah! Dick graphs etc. The Instagram links in this post connect with individual illustrations.

I found Mona Chalabi through her illustrated New York Times article (7 April, 2022) **9 WAYS TO IMAGINE JEFF BEZOS’ WEALTH.**

So Jeff Bezos personal wealth is $172 Billion (US$) Her Toblerone Block vs Mt Everest comparison was in this article.

NOTE: Median wealth is the mid-point wealth ie. 50% of Americans have more wealth. 50% of Americans have less wealth.

Mona also includes relevant the data in her posts. eg.

This idea comes from Burkard and Giuseppe @ the fabulous MATHOLOGER channel. Students can make a pattern called a cardioid that pops up all over math according to Burkard.

Follow these steps. There is a pdf file below the first diagram for printing exercise sheets.

And then watch the MATHOLOGER video for a really interesting explanation.

**x2 Tables on a Circle pdf file for printing**

**This circle graph blank could also be used for x3 and x4 tables, ****which produce totally different yet equally amazing patterns.**

Halfway there, now it gets tricky. +52 to each point on the circle and keep multiplying by 2.

ie. 27 x 2 = 54, 28 x 2 = 56 and so on.

so 0 = 52, 1 = 53, 2 = 54, 3 = 55, 4 = 56 etc

This shape is called a CARTIOID.

**Nathan Chen, 22, USA, wins GOLD in the Men’s Figure skating with 5 brilliant, soaring quadruple jumps executed to perfection to Elton John’s “Goodbye Yellow Brick Road” and “Rocket Man.”**

**According to the fab NBC video, Mathletes, nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.**

This is a typical figure skating score card for one competitor.

The final score, however, is based on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

**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:

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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:

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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:

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That’s about right.

**While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.**

**The significant maths for ski jumpers is therefore X-section area.**

**Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!**

**Ski jumpers increase their speed going down the ramp by reducing their X-section area:**

**Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum angle.**

**Here is the formula for Air Resistance of Drag:**

*D *= ½*CApv ^{2}*

**Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.**

*A* is the X-section Area,

*p* is the density of the air and

*v* the velocity of the object.

**More here.**

**As Abby Hughes has tripled her X-section area in the air, she will ****have tripled the vertical drag during her jump. This will slow here decent.**

*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for projectile motion from Wired magazine.

The equation for projectile motion also applies to **Motorbike Jumps** and **Longbow Arrows**.

Here is the x-y graph for different launch angles.

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a