OMG! Credit Card Antenna Geometry is so cool + some PIN Probability

The world  has mostly agreed on the size of a credit card:

Credit cards today contain a microchip and aerial.

A credit card is dissolved in ACETONE (solvent found in some nail polish removers) to extract the chip & aerial in this BBC video.

 

OMG! The cardless chip still works to pay for coffee. But if you wanted cash you would still need the PIN.

FOR THE LONGEST KICK or THROW in Football you need this MATHS

………………………………………………

The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

NATHAN CHEN wins Gold but Figure Skating Scores can be BAD MATH

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.”

Nathan Chen’s Winning Performance on You tube HERE.

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.

Tessa Virtue and Scott Moir(Above) GOLD Medal performance at Pyeongchang 2018 here.

Kailani Craine, Australia

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.

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

Skater A:

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

7.00 + 7.00 + 7.00 + 6.75 + 7.00

……………………………………..

=  34.75/ 5 = 6.95

Skater B:

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:

7.00 + 7.25 + 7.00 + 7.00 + 7.00

……………………………………..

=  35.25/ 5 = 7.05

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!!!!

Death by Chocolate: Yes! Chocolate can kill. But how much would kill you?

 Choco Yum Yum! Mathspig lervs chocolate. But did you know chocolate can kill you?

Chocolate contains a chemical called Theobromine. This alkaloid ( other alkaloids include cocaine, nicotine, caffeine, and strychnine) can kill humans. More info Wired Magazine.

How much chocolate is too much?

Firstly, the darker the chocolate the more Theobromine it contains.

According to About Chemistry based on the highest possible toxicity:

* Vetmedicine: Cooking chocolate contains 8-10 times the Theobromine in Milk Chocolate.

According to Wired large doses of theobromine may cause “nausea and anorexia ….. sweating, trembling and severe headache.”

The Royal Society of Chemistry notes that chocolate does not contain caffeine, but theobromine induces similar symptoms.

LD50 for the lethal dose for 50% of the population for Theobromine is:

1000 mg/kg 0r 1gm/kg of body weight in humans

Death by Chocolate Calculations:

1. FORMULA

2. GRAPH

3. Percentage

Death by Chocolate for CATS

Chocolate contains a poison called Theobromine.

LD50 for  Theobromine for cats is 200mg.

LD = Lethal Dose. LD50= Lethal Dose for 50% of the population. Cats in this case. This is how poison toxicity is measured. 

According to The Royal Society of Chemistry, cats are hypersensitive to Theobromine but, as cats cannot taste sweetness, they are rarely poisoned.

Real World Maths: %, vaccines and saving humanity

The following information comes from the article 2 Companies Say Their Vaccines Are 95% Effective. What Does That Mean? Carl Zimmer, New York Times, 20 Nov 2020.

See Principles of Epidemiology here.

As Dolly Parton donated $1Million to Moderna, the vaccine research group, it is only appropriate to include a VACCINE parody of her hit song, Jolene put together by the Dept of Health, AUSTRALIA.

Real World Maths: Gotye and Some $$ that he got to know

Melbourne singer, songwriter, and geometrically inclined performer Gotye performing with Kimbra won 3 Grammy Awards for his song Somebody that I used to Know in 2013.

The Gotye youtube clip has had 1,535,344,012 or 1.5 Billion hits since it was first uploaded 5th July 2011. 

Mini Rates Exercise:

In 111 months Somebody that I used to know has scored 1.5 Billion hits. How many hits a. per month, b. per day, c. per minute? (Round off numbers)

Ans: a. 13.5 Million per month

         b. 450,000 per day (Assuming 30 days per month)

         c. 37,500 per hour and 625 per minute (for over 9 years non stop!)

Estimate of Youtube Earnings for this Song:

The Influencer Marketing Hub puts the rates an advertiser pays between $0.10 to $0.30 per view on Youtube, but averages out at $0.18 per view. Using the lower rate, how much has this song earnt in just over 7 years?

Earnings = 0.10 x 1.5 x 10⁹  = 1.5 x 10⁸     = $150,000,000  = $150 million*

*This calculation is based on a click per view of the video.  Gotye will not receive anything like $150M, however, because advertisers pay per click on their ad.

According to the Influencer Marketing Hub again ‘on average, the YouTube channel can receive $18 per 1,000 ad views. This equates to $3 – $5 per 1000 video views.’ Again, using the lower rate:

Video Hits =1.5 x 10⁹

Divide by 1,000 = 1.5 x 10⁹ ÷10³    = 1.5 x 10⁶

$3.00 per 1,000 video clicks earnings = 3.00 x 1.5 x 10⁶   = 4.5 x 10⁶

Realistic Earnings = 4.5 x 10⁶    = $4,500,000  = $4.5 million

A Geometric Parody:

Here is Mathspig’s take on the song:

Somebody that I used to Know:

It’ll either help students do their exercises or work like Clockwork Orange and have them running screaming out of the room when they hear the first few notes.

Real World Maths: Fractions & Guitar Sizes

Guitar Gear Finder.

Cool kid plays Stairway to Heaven solo!

Crazy Math: How to survive a Wagon Wheel Rolling over your head

There is some amazing Middle School Maths in The Cake Server on Joseph’s Machines. 

eg. Calculate the length of the arc of a circle to fit your HEAD! Watch for it.

Besides, this is so much FUN!

1. Stuntman Math: Car Stunts

“With enough stupidity you can get any car to roll over” (MSN AUTO)

What stuntmen and women need is maths!

Maths is essential to the process, from calculating speeds and braking distances to looking at the ratio of the amount of film shot to the length of time of the end sequence. The stunt and crash is outlined, and the co-ordinator explains how he must calculate speeds and stopping distances carefully.

So you want to be a stuntman?

First think of the pain.

Mark Eiden, 52, a professional stuntman (pictured) who is not only afraid of heights, but was once told he likely wouldn’t walk again. Eiden’s had surgery on both arms and shoulders, five knee surgeries, six nasal reconstructions, foot and hand surgery and a facial cast. He fell off the top of a stunt car at 40 mph when the tyre blew. He gaffer taped his ear and continued, despite severe concussion. Northern Express Michigan

If you still want to be a stuntman do the Maths:

Rolling a Car:

You can use quick handbrake turn, speed around a corner, fishtail into the curb or some other lunatic thing. The most controlled way to roll a car is to use a ramp.

These ramps often have a kicker at the end to add extra lift. Ramp calculations can be complicated, but the simplest way to look at the maths is to determine the angle a car will roll ie. When the Centre of Gravity moves over the base.

Centre of Gravity vs Base Width

The distance between the front wheels in cars is often called the track width.

Table from Accident Reconstruction Website

So the Lamobgini Diablo is very hard to roll (build a higher ramp) and it therefore beats the SUV for stability every time.

Balancing on 2 Wheels

A more skilled stunt involves driving a car on two wheels. A very skilled stunt driver can lift the car onto wheels by snaking the car back and forth across the road until it balances on 2 wheels.

From the Centre of Gravity vs Base angles above you can see that the SUV is the easiest car to balance of 2 wheels.

But there is nothing quite as crazy as this SUV stunt:

Saudis changing car tyres, just insane.

View full video here.

Safe Driving Info here