Activity: Dropping a Coin onto a Grid

Activity: Dropping a Coin onto a Grid

coin 1750
A few hundred years ago people enjoyed betting on coins tossed on to the shock … would they cross a wrinkle or not ?
A man ( Georges-Louis Leclerc, the Count of Buffon, see “ Buffon ‘s Needle “ ) started thinking about this and worked out how to calculate the probability .
nowadays it is your twist to have a go !

You will need :

us 1 penny
1 euro india 5 rupee
A small round coin ,
such as a US penny, a 1c Euro or 5 Rupee .
grid A sheet of paper with a grid of 30 millimeter squares .

Steps

  • Measure the diameter of your coin: ____ mm
    • a US Penny is 19mm, a 1c Euro is 16.25mm, a Rs 5 is 23mm
  • Also measure the spacing of your grid (it may not print at exactly 30mm): ____ mm
  • Put your sheet of paper on a flat surface such as a table top or the floor.
  • From a height of about 5cm, drop the coin onto the paper and record whether it lands:
    A : wholly inside a square ( not touching any grid lines )
    bacillus : Crosses one or more lines
    grid: coin A inside, and coin B on

The accurate height from which you drop the coin is not important, but do n’t drop it so close to the newspaper that you are cheating !
If the mint rolls completely off the composition, then do not count that go .

100 Times

now we will drop the mint 100 times, but first …
… what percentage do you think will land A, or B ?
Make a estimate ( estimate ) before you begin the experiment :

Your Guess for “A” (%):  
Your Guess for “B” (%):  

OK let’s begin .
Drop the coin 100 times and record A ( does not touch a line ) or B ( touches a line ) using Tally Marks :

Coin lands Tally Frequency Percentage
A      
b      
  Totals: 100 100%

now draw a Bar Graph to illustrate your results. You can create one at Data Graphs ( Bar, Line and Pie ) .

  • Are the bars the same height?
  • Did you expect them to be?
  • How does the result compare with your guess?

We Can Calculate What It Should Be …

hera are some positions for the coin to land so it does not quite touch one of the lines :
coin grid inside different positions
Place your coin on your grid ( like above ), and then put a bell ringer on the wallpaper where the plaza of the coin is ( fair a harsh estimate will do ) .

coin grid radius See how the mint ‘s center is one radius r away from a line.

( Read about a Circle ‘s Radius and Diameter. )

Make lots of “ center marks ” then draw a box connecting them all like below :
coin grid 30-d
d = Coin ‘s diameter ( 2 × roentgen )
When a coin ‘s center is within the yellow box it wo n’t touch any line .
The chicken box is smaller than the grid by two radiuses ( = one diameter ) of the mint .
So what are the areas ?

  • The area of the grid square is 30 × 30 = 900 mm2
  • The area of the yellow box is (30-d) × (30-d) = (30-d)2 mm2

The above calculation was for a 30 millimeter grid, but we can use S for power system size :

  • The area of the grid square is S × S = S2 mm2
  • The area of the yellow box is (S-d)2 mm2

Example: A 1c Euro (d=16.25 mm) on a 29mm grid (S=29 mm):

Grid Square = 292 = 841 mm2
yellow Box = ( 29-16.25 ) 2 = 12.752 = 162 mm2 ( to the nearest mm2 )
So you should expect the coin to land not crossing a line of the grid approximately :
“ A ” = 162 / 841 = 19.3 % of the time
And “ B ” = 100 % – 19.3 % = 80.7 %
now do the calculations for your own grid size and coin size .

Grid Spacing second (mm):  
Diameter of Coin five hundred (mm):  
Area of Grid Square = S2 (mm2):  
Area of Yellow Box = ( S-d ) 2 (mm2):  
“A” (%):  
“B” (%):  

How do these theoretical results compare with your experimental results ?
It wo n’t be claim ( because it is a random thing ) but it may be finale .

Different Sizes of Coin

Try repeating the experiment using a different sized mint .

  • First calculate the theoretical value … how does this affect the values for A and B?
  • Then do the experiment to see how close it gets.

What You Have Done

You have ( hopefully ) had fun running an experiment.

You have done some geometry, and had some experience calculating areas and probabilities .
And you have seen the relationship between theory and world .

reference : https://ontopwiki.com
Category : Finance

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