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.
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:
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.
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
As this jump – as in most base jumps – involves a standing start:
This is a repost of Mathspig’s very popular Stuntman/woman series.
Star Stuntmen
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.”
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.
Mathspig Blog 
