Archive for high school mathematics

métro static

Posted in Kids, Travel with tags , , on March 26, 2014 by xi'an

[heard in the métro this morning]

“…les équations à deux inconnues ça va encore, mais à trois inconnues, c’est trop dur!”

["...systems of equations with two unknowns are still ok, but with three variables it is too hard!"]

\STATE [algorithmic package]

Posted in Books, Kids, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , on June 8, 2012 by xi'an

I fought with my LαTεX compiler this morning as it did not want to deal with my code:

 \begin{algorithmic}[1]
 \STATE N=1000
 \STATE $\hat\pi=0$
 \FOR {I=1,N}
 \STATE X=RDN(1), Y=RDN(1)
 \IF {$\text{X}^2+\text{Y}^2<1$}
 $\hat\pi$ = $\hat\pi +1$
 \ENDIF
 \ENDFOR
 \RETURN 4*$\hat\pi/$N
 \end{algorithmic}
 

looking on forums for incompatibilities between beamer and algorithmic, and adding all kinds of packages, to no avail. Until I realised one \STATE was missing:

 \begin{algorithmic}[1]
 \STATE N=1000
 \STATE $\hat\pi=0$
 \FOR {I=1,N}
 \STATE X=RDN(1), Y=RDN(1)
 \IF {$\text{X}^2+\text{Y}^2<1$}
 \STATE $\hat\pi$ = $\hat\pi +1$
 \ENDIF
 \ENDFOR
 \RETURN 4*$\hat\pi/$N
 \end{algorithmic}
 

(This is connected with my AMSI public lecture on simulation, obviously!)

cannonball approximation to pi

Posted in Statistics with tags , , , , , on October 8, 2011 by xi'an

This year, my daughter started writing algorithms in her math class (she is in seconde, which could correspond to the 10th grade). The one she had to write down last weekend was Buffon’s neddle and the approximation of π by Monte Carlo (throwing cannon balls was not mentioned!). Here is the short R code I later wrote to show her the outcome (as the class has not yet learned a computer language):

n=10^6
counter=0
#uniforms over the unit square
ray=runif(n)^2+runif(n)^2
#proportion within the quarter circle
conv=cumsum((ray<1))/(1:n)
plot(conv,type="l",col="steelblue",ylim=c(pi/4-2/sqrt(n),
     pi/4+2/sqrt(n)),xlab="n",ylab="proportion")
abline(h=pi/4,col="gold3")

and here is an outcome of the convergence of the approximation to π/4:

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