Archive for the ‘Real Life Math’ Category

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3D Random Walk Math . . . . . . . . . . . . for Middle School

July 6, 2021

Random Walk math is both simple and complicated all at the same time. The math models are a little bit complicated but the concept is simple. 

Random walk math is used to model many processes in Chemistry, Physics, Biology, Zoology, finance (Stock market movement), psychology, ecology,  computer science, and video games.

Simple Example:

Choices: Up, Down, N, S, E, W.

Note: We are still using constant step size and right-angle turns.

The random walk of one particle would look something like this from Mathworld:

In an infinite no. of steps the probability of reaching the starting point again is 0.3405373296 or about one-third. Mathematicians use math models to calculate the probability of a particle ending up here or there or back where it started. eg. It is less likely that the particle above would move in a straight line 500 times in a row. 

You can play with a 3D random walk generator here.

And check out this excellent video explaining a 3D Random Walk in nature.

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How the UK Aced Covid, sort of …

June 29, 2021

London yesterday. Spectators give a spontaneous standing ovation to Oxford Professor Sarah Gilbert (below), who was one of the scientists involved in developing the Astra-Zeneca vaccine and one of 100 key worker special guests on opening day. (The Age, 29 JUN, 2021)

Here are the Covid-19 Vaccination stats for the UK as of yesterday:

BBC, 29 JUN 2021

The UK recorded 22, 868 cases yesterday, but only 3 deaths.

The last time the UK recorded close to 23,000 cases was on 16 December 2020. That day, 613 deaths were announced. (The Age, 29 JUN 2021)

In 2019, in the UK, the total death toll was 616,014 or 1688 per day. Tragically but realistically elderly patients with multiple health issues are more likely to contract Covid and die from complications exacerbated by Covid-19 but not necessarily caused by the virus.

The death toll numbers are now encouragingly low in the UK despite the high infection rates from the highly contagious Covid Delta variant.

UPDATE:

On 9 July 2021, the UK recorded 35,707 cases and 29 Deaths. According to  Worldometer stats  (below), the case numbers and deaths are still rising. Too soon to celebrate even though the UK Freedom Day is only 10 days away.

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Toilet Paper FUN FACTS Maths

June 1, 2021

Mathspig is in Melbourne, Australia. We’re in Lockdown. AGAIN!

And toilet paper has disappeared off the supermarket shelves. AGAIN.

So today we are doing maths based entirely on toilet paper using information from the Toilet Paper Fun Facts website. Yes! It exists here.

Toilet Paper Fun Facts Website

Protractor Wind Speed Calculator

POP UP ANS Q 1 & 2 Yr 7&8 Toilet Paper fun facts

Traxxas XO-1 Website

Pythagoras Equation Diagram here

Here is the Sine Rule (Watch 1.5 mins)

Check sine curve here:

Listen to sine curve here:

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Simple Math with a KO Punch

March 24, 2021

So often MATH makes clear what politicians fail to see. This is a cartoon in the Boston Globe by Dan Wasserman.

Follow Dan on Twitter @WassermanToons

The minimum wage in Australia is currently  $19.84 per hour for 21yo+. This is USA $15.08.

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2. Stuntman Math: Jumping off a Building

October 14, 2019

This is a repost of Mathspig’s very popular Stuntman/woman series.

The main concern when jumping off a building is that the airbag (cardboard boxes) cover the drop zone.

The maths calculations involved in jumping off a building are straightforward. You might like to check out How Maths Solved a real murder.

Jump Height that Kills

It doesn’t take much of a fall to cause damage. Sean Hughes, professor of surgery at Imperial College, London. Says “From a height of 3m you could fracture your spine,” he says. “At around 10m, you’re looking at very serious injuries.” (The Guardian, 20 MAY 2014)

Stunt Jump from building from standing start

1 stunt jump from building

As this jump – as in most base jumps – involves a standing start:

2 Mathspig Jump off building

Airbagsupplies.

Stunt jump from building running

We will assume you are no Usain Bolt. His running speed, the fastest in the world, is 44.72 km/h (12.42m/s, 27.44 mph).

We’ll say your running speed on take-off is:

Vy = 15 mph = 24.1 kph = 6.7 m/sec

3 Mathspig stuntman running jump

Don’t do this at home.

NB: Airbag dimensions: 20m x 20m x 4 m

Handstand of death

Would you jump off a 25 story building?

Watch on Youtube here.

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3. STUNTMAN MATH: Motorbike Jump

October 9, 2019

This is a repost of Mathspig’s very popular Stuntman/woman series.

Star Stuntmen

Picture 2

Star Stuntmen Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”

1. perlin_stunt_ Terminator 3

Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman

Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.

2 Evel Knievel JUNE-23-1973

His injuries are legendary:

3 the-many-injuries-of-evel-knievel1

More Evel Knievel

Ramp Design

4 Ramp Design Angle of final kicker

The angle of the kicker in ramp design can vary from 100 – 700 (See below)

5 Robbie Maddison's 2008 New Year's Eve jump Arc de Triomphe at the Paris Las Vegas

Picture 2

 

Moto-X Ramp Jump Maths

6 motorbike -parabola Mr Reid

7 bike jump 1 Method 1



8 bike jump Method 1 final

 

9 bike jump method 1 final

 

Picture 2


10 bike jump method 1 final

 

As any bike nut knows increasing speed and angle of take off will increase jump distance.

Here is a graph from final gear for speed vs angle to jump 90m.

12 optimising ramp angle

 13bike jump Method 2

METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.

You will find a thoroughly detailed calc for STUNT JUMP MATHS here:

And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here.