Archive for the ‘Real World Math’ Category

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Maths in the Real World: 10 Attention Grabbers for Middle School

September 5, 2021

1. Smoke Jumpers: The Amazing Maths of wildfires

 

USA UNITS HERE

 

METRIC UNITS HERE

 

2. The Rolling Coin Paradox!!

ROLLING COIN PARADOX HERE

 

3. How barcodes work!

Barcode MATHS HERE

 

4. Pop Song Beats and Jogging

 

Pop Song Beats and Jogging MATHS HERE

 

5. Linear Math and Linear Drumming. It’s a thing!

 

Linear Math and Linear Drumming. HERE

 

6. Powers and the Loudest Rock Band in the World

Powers and the Loudest Rock Band MATHS HERE

 

7. Alcohol Kills! Calculate how much would kill you!

Alcohol Kills! MATHS HERE

 

8. Tall Tales: Is height the most important factor in sport?

Height in Sport maths: USA UNITS HERE

Height in Sport maths: METRIC UNITS HERE

 

9. Mmmmm! Chocolate. Yes! It can kill  you

Chocolate. Yes! It can kill  you MATHS HERE

 

10. Random Music? You think!

 

Random Music?MATHS HERE

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Car Crash Maths: Saved by a millisecond

August 22, 2021

*In 1970 the Victorian Government made the wearing of seat belts compulsory.

*The first government in the west to do so.

 *Within 14 months the other Australian states followed.

*The road toll in Australia dropped:

   1969       3,382 road deaths per year

   1988       2,887 deaths

   2018      1,135  deaths

Mathspig lived on a country police station before seat belts became compulsory and a number of kids she went to school with died in car accidents.

Three factors have reduced the road toll in Australia:

1. Wearing seat belts

2. Stopping drink driving

3. Introducing Airbags (from 1980s)

Our eyes can easily detect the blink (above) set a 300ms.

Ditto, the light flash (below), which is set to flash at  200 ms but it will drive you CRAZY if you look at it for too long.

The fabulous video (below) will show you the amazing details of the ms timing that saves lives in a car crash. You will see real car crash tests. And the frightening results too.

It was made by an engineer who worked for GMH or Holden as we call it in Australia. 

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A Bitcoin Bubble, a Random Walk and a blind-folded Monkey

July 6, 2021

What is all this monkey business? It started in 1973 when Princeton University professor Burton Malkiel claimed in his bestselling book, A Random Walk Down Wall Street, that “A blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.”

In other words, the stock price movement is random. 

See Forbes Magazine here.

Now in its 12th edition, the book tackles Investment Bubbles including Bitcoin. Is there a Bitcoin Bubble? According to the ABC on 24 MAY 2021 this was the Bitcoin Bubble Graph:

From the ABC news here

Random Walk Game

So can you beat the financial market? Try this 2D Random Walk game (pic below) to see if you can guess the next random move and beat the system.

In the game, you have to remove gold blocks by clicking on blocks in the way of the moving green dot, but you lose energy (lose money, perhaps) each time you remove a block.  Can you guess where the green dot is moving? Can you survive? Mmmmm! Good Luck. You’ll need it.

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Real World Maths: The Zodiac Murders Cipher Cracked after 51 years

December 17, 2020

Mathspig can remember the horror of the ZODIAC MURDERS in California in 1968-69. 

1969 was a very big year for psychopaths as the creepy Sharon Tate Murders by Charles Manson and his ‘Family’ also happened that year.

The ZODIAC murderer, who killed, at least, 5 people and sent encrypted messages to the San Francisco Chronicle, has never been caught. After 51 years the 340 cipher with 340 characters (below) was cracked last week.

The 340 cipher was cracked by of Jarl Van Eycke, David Oranchak, and Sam Blake, computer programmers and codebreakers from Belgium, the US, and Australia. Sam Blake is a Melbourne Mathematician.

You will find everything you need to know about these codebreakers at The Nerdist Blog here.

The ZODIAC murderer used all 3 Cipher Methods (See blog Above) to write the cipher.

The Zodiac combined a PIGPEN style cipher with a PLAYFAIR type cipher. The code breakers knew the key (below) from other ZODIAC messages.

The problem was the TRANSPOSITION Rule. The codebreakers’ programs had to sort through 650,000 possible reading directions to find the correct one for the cipher.

The diagonal of … include two-letters across, move down one row, then include the next two letters across, repeat, seemed to produce words.

The breakthrough came when Sam Blake divided the cipher into three blocks.

Finally, the message could be read. The ZODIAC murderer was a complete PSYCHOPATH, who thought he was collecting slaves for the afterlife!!!!!!!

If you are intrigued by this story then you will find these two videos by David Oranchak very interesting.

 

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Real World Maths: Surds and all that jazz …

November 23, 2020

Eddie Woo is an Aussie Maths teacher who runs his own Youtube Channel. So popular is this channel in October 2015, Woo won the NSW Premier’s Prize for Innovation in Science and Mathematics. This youtube clip won’t tell you where you will use surds, but it does something magical.

It compares surds to different kinds of music to help students understand why mathematicians go crazy over the concept of surds. This clip tells why maths is soooooo special. There is no guesswork or fake information in this maths. Maths must be accurate. And surds demonstrate this point. (Look for the 5 min mark)

Will you use surds in real life?

Maybe. Probably, not. But surds are used in mathematical programs that demand accuracy. eg. engineering skyscrapers, building satellite dishes, and even in video games. But you won’t see them. Like so much mathematics surds will be hidden in some algorithm.

Here are two Examples:

1. The Golden Ratio:

Often written a 1:1.61 the Golden Ratio or Fibonacci Sequence appears in art and nature and has an aesthetic appeal to the eye, but the accurate ratio is:

2. The Quadratic Function

Satellite dishes, headlights, torches, and bridges all designed using the parabolic arc. The parabola is defined by the quadratic function and sometimes solving for x produces an irrational no. namely a surd. Rounding off can introduce inaccuracies that can become more dramatic when scaled up to the sie of, say, a bridge. 

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

November 12, 2020

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 10 = 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 10÷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:

some-triangles-i-used-to-know 2

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.

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Real World Maths: Powers and the LOUDEST Rock Band in the world

October 22, 2020


Hellooo mathpiggies, I said HELLOOO MATHSPIGGIES.

Who has been to a rock concert recently? Like, NO ONE!

Studies show, however, that adolescents often suffer temporary (sometimes permanent) hearing loss after going to a 3 hr rock concert in rows up to 18 away from the stage.

teen beat box

Rock Concerts Cause Temporary Hearing Loss in Teens


Deep Purple: The Loudest Rock Band Ever

Lime Cordiale, a popular band in Australia

Find dB answers here.

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Real World Maths: Geometry, Heavy metal + Headbangers Heads

October 4, 2020

Are Headbangers Neck Wreckers?……..

Check out the Maths!


pic 1 headbanging-AWG4JT_188x156

The NHS reports that Australian Researchers Declan Patton and Andrew McIntosh, Uni of NSW, have conducted a study into brain and neck injuries of headbangers published in the British Medical Journal.

pic 2 headbanger hair pic

Concerts included as part of the study included Motörhead, Mötley Crüe, Skid Row, The Hell City Glamours, L.A. Guns, Ozzy Osbourne, Winger, Ratt, Whitesnake, and W.A.S.P.

Here’s Motorhead with a ‘nice’ moshpit.

motorhead

140 BPM for Ace of Spades. Motorhead BPM range is 91 – 203 

The Headbanger Study Concluded:

1. Head movement of more than 75o for an average heavy metal beat will cause head and neck injuries. This movement causes headache and dizziness.

 2. Beats above 130 bpm (beats per minute) cause neck injury.

The average headbanging song has a tempo of about 146 beats per minute (bpm).

and according to Mathspig:

3. Being punched up in the mosh pit. Do you need maths for that conclusion?

Researchers recommendations:

1. Reduce range of head and neck movement

2. Headbang to a  slower tempo

3. Wear a neck brace. (Isn’t a bad hair cut enough?)

Headbanger Rates Exercise:

How many headbeats per song of 5mins would a headbanger manage for the following song tempos?

Mathspigs excited. Look there is a band called Mutemath!!!!!!!! And here they are:

mutemath

……………………………………………………………………………

Just to show that there is something spookily primitive about headbanging here is Headbanger Baby:

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Real World Maths: Linear Graphs and Linear Drumming

September 21, 2020

Taylor Hawkins Foo Fighters drum solo

 

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Real World Maths: RATES, pop song drumbeats and jogging

September 17, 2020

Jog FM Here are songs with bpm = 100