Archive for the ‘Uncategorized’ Category

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Don’t play it again Sam! The iPod, iPad & iPhone Shuffle

June 7, 2019

Here is an example of Gambler’s Fallacy, but for non-gamblers. 

We see – in this case – hear a pattern and then attribute meaning to this pattern  – It’s a conspiracy!!!! – when there is no pattern and no meaning!!!!! So Apple found when designing their iPod shuffle feature later on the iPad and iPhone. 

“When Apple first introduced the shuffle feature on its iPods, the shuffle was truly random; each song was equally likely to be picked than any other. However, the randomness didn’t appear random, since some songs were occasionally repeated, and customers concluded that the feature contained some secret patterns and preferences. As a result, Apple was forced to revise the algorithm. ‘We made it less random to make it feel more random,’ said Steve Jobs, the CEO of Apple’  

p68 The Decisive Moment How the Brain Makes Up Its Mind Jonah Lehrer (Text Publishing 2009)

dice

Try it. Pick 12 songs maybe off your playlist  – Your MP3 player, perhaps or a Top 20 Chart or Top 20 Downloads Chart – assign each song a number: 1, 2, 3….up to 12. Take two dice (Diehards Note:  It’s 1 die, 2 dice) and roll.

How many throws until you get 2 songs played in a row?

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The Terrifying Math of Running from a Bear … USA Units

May 14, 2019

USA UNITS below. METRIC UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:  550 lb        

Height:  8’ 2”   

Top Speed: 35 mph  =   51 ft/s    

Brown Bear

Weight:  1,500 lb       

Height:  8’ 2”              

Top Speed: 22 mph  =  32 ft/s     

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 27 mph  =   40 ft/s     

Bears are not dangerous:

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In fact, more Americans die each year from choking on their own vomit than are killed by bears.

More death stats here

Nevertheless, bears are very fast. So you can see why Park Rangers offer the following advice:

More information at Mountain Nature.

The reason for waiting until the bear is 15 ft away is to make sure the spray doesn’t disperse in the air. If the Pepper Spray is too spread out it will not stop the bear.

Ref: Dog helps save hikers after grizzly chases them for 20 minutes.

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The Terrifying Maths of Running from a Bear … Metric Units

May 14, 2019

METRIC UNITS below. USA UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:   250kg

Height:   250cm

Top Speed: 56kph  =   16 m/sec

More bear stats here. 

Brown Bear

Weight:  680kg

Height:   250cm

Top Speed: 35kph  = 10m/s

More bear stats here.

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 243kph =   12m/s

So Usain Bolt could out run a Brown Bear but NOT a Grizzly!

Bears are NOT as dangerous as:

In fact more Americans die choking on their own vomit each year than a re killed by bears.

More death stats here.

But bears are very fast so Park Rangers recommend the following survival tactics:

More bear survival info here.

REF: Dog helps save hikers after grizzly chases them for 20 minutes here.

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Sharp Shooter Maths …. METRIC

May 10, 2019

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Australia has a very strict gun laws today. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against our fridge. He pocketed the magazine.

A .22 means a bullet calibre of .22 inches.

My Dad the Sharp Shooter stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more. More on my childhood here.

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Sharp Shooter Maths

One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  The MOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

As the distance away from the target increases the target zone circle area increases.

A sharp shooter would be considered very skilled if they can shoot within a target zone (circle) of 10.5 inch radius at 1000 yds. Hitting a bull’s eye at this distance is down to luck.

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Medals, Meglomaniacs and Sharp Shooters…….. The Maths METRIC

May 10, 2019

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question

‘Could medals protect the wearer from a sharpshooter?’ 

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

 

The target zone (circle) had a diameter of 1.9cm. This is smaller than the diameter of an American Quarter, an Australian 10c and a UK pound all of which have a diameter of appro 2.4 cm.


So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.

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Which sport is more DANGEROUS to play? Cricket or baseball?

April 22, 2019

Reposted due to popular demand.

Mathspigs you are about to be hit on the head with some BALL PARK figures. There is so much maths involved in comparing cricket and baseball I hardly know where to begin. So I will just set you up with comparative statistics for starters. Here they are:

cricket and baseball stats mathspig

You now have sufficient information to calculate the following:

cricket 1_tnsQ1. If a cricket player  makes 4 runs (and runs between the wickets) and a baseball player hits a home run, who runs the furtherest?

ANS: 4 runs in cricket distance = 80.48 m

Home run in baseball distance = 109.6 m

Q2. What are the delivery ball speeds of an average pitcher and a mid paced bowler in m/sec?

ANS: Average Bowler Ball Speed = 110 – 125 km/h = 30.5 – 34.7 m/sec

Average pitcher Ball Speed = 80.47 km/h = 22.4 m/sec

Q3. How far would the delivery of an average pitcher and a  medium paced bowler travel in 10 seconds?

S = d/t

t = 10 secs:

d = S x t = S x 10

ANS: In 10 sec a ball bowled by an average bowler would travel 305 – 347 M

In 10 sec a ball thrown by an average pitcher would travel 224 m

baseball_01_tns Q4. If Shoaib Akhar fielded a ball in cricket 20 m from the wicket when the batsman was still 8m from the wicket (A typical running speed for humans is 32 km/h) would he be able to run him out?

Akhar ball speed S = 45.0 m/sec

d = 20 m

S = d/t

t = d/S

t  = 20/ 45.0

t = 0.44 secs

Batsman Speed = 32 km/h = 8.9 m/sec

How far can the batsman run in 0.44 secs?

d = S x t

d = 8.9 x 0.44 = 3.9 m

So batsman would be easily run out by Akhar as he is 8 m from the crease.

 Q5. How long would it take a ball thrown by Joel Zumaya to reach the batsman if the pitchers mound was exactly in the middle of the baseball square?

ANS: Speed of ball pitched by Zumaya = 168.65 km/h = 46.8 m/sec

Zumaya speed ball

shane warne cricketline

 

 

 Q6. Which sport is more dangerous?

We will base our calculations on the speed (or velocity) and the weight (or mass) of the ball. We must use the same units in all calculations. For each sport plot x-axis: velocity of ball (v) against y-axis mass x velocity (mv) of the ball. mv is the momentum. In ballistics the change in momentum is called the IMPULSE (impact for us). If you are hit on the head with a ball it is the change in momentum of the ball that does the damage. A small ball at a high speed can do as much damage as a larger ball at a slower speed. We are not including spin, curve balls or air resistance to keep calculations straight forward … literally!!! 

Cricket baseball ball IMPACT mathspig

cricket vs baseball impact mathspig

Now that you have your graph you can answer these questions:

tim_lincecum_101mphQ6a. Which sport for professional players is the most dangerous? 

You will have to look at the graph. A cricket ball is heavier than a baseball BUT the fastest pitchers can pitch a ball slightly faster than bowlers can bowl.  IMPACT (mv) depends on multiplying mass by velocity. You will see the stats for Akhar and Zumaya marked on the graph and you can use these stats to estimate impact.

BUT then there is the impact of batting, which increases the velocity of the ball. That will have to wait for another post.

Q6b. At what speed does a cricket ball do the same damage as a baseball? Give one example.  (Hint: Draw a straight line from the Y-axis)shoaib akhtar thaindian

Once again look at the  graph above!

You will find more maths on impact on Mathspig:  for a punch here and from hailstones here.

 

Pics: Tim Lincecum (Left) with 101 mph pitch, Shane Warne (Upper Right) and Shoaib Akhtar (Lower Left)

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Giant Easter Egg Math … USA units

April 5, 2019

Good News for Chocoholics

To get the right texture Easter Eggs are made from sugar or sucrose and not from corn syrup. But chocolate contains lots and lots of sugar.

Guylian sea shells

………………………………………………..

Guylian Sea Shells:

Weight Sea Shell: 4.23 oz

Weight Sugar: 1.69  oz

% sugar = 1.69/4.23 x 100 = 40%

………………………………………………………………..

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Guylian luxury easter egg

This is a Guylian Luxury Easter Egg. It can also be used as a designer handbag, I guess.

Guylian Easter Eggs:

Weight Easter Egg: 3.53  oz

Weight Sugar: 1.83 oz

% sugar = 1.83/3.53 x 100 = 52%

You’ll find nutrition data here.

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Easter Challenge:

You will find the largest Chocolate Easter Egg ever here.

This egg is 34 ft 1.05 in high and weighs 15,873lbs, but  it is ugly.

I like the GUYLIAN GIANT EGG (below) because it looks good and we know exactly how much sugar is in this egg. Mathspig Big Easter Egg

This Giant Egg was made in 2005 in Belgium by chocolate maker Guylian.

Statistics:

Height:  27 ft

Weight:  4300 lb Chocolate

No. Chocolatiers: 26

No. Chocolate bars: 50,000

Total time: 525 hrs

Easter Challenge for Chocoholics

fiat punto 1The amount of sugar in the giant egg weighs as much as a Fiat Punto.