float buffon(int N, float needleLength){ // This should implement the buffon method to estimate Pi. // you can use gRandom->Uniform(0,1) to get uniformly distributed numbers. return 3.14 } float alternative(int N){ // This should implement the alternative Version. return 3.14 } int ex12 (){ //First we show, that the principle is working int N = 100000; float needleLength = 1.; cout << "Proof of Principle." << endl; cout << "Pi is : " << endl; cout << TMath::Pi() << endl; cout << "Buffon Method says: " << endl; cout << buffon (N, needleLength)<< endl; cout << "Alternative Method says: " << endl; cout << alternative(N) << endl; //Now lets make some double logarithmic plot to guess the speed of conversion. //Unfortunately it turns out the differences are quite small, except for extreme needle length and one method is clearly better than the other... static const int lengthSteps = 5; static const int ordersOfMag = 40; float xList[lengthSteps+1][ordersOfMag]; float yList[lengthSteps+1][ordersOfMag]; for (int ii = 0; ii < lengthSteps; ii++){ for (int jj = 0; jj < ordersOfMag; jj++){ xList[ii][jj] = int(10 * pow(1.2, (jj+1))); yList[ii][jj] = fabs(buffon(int(10 * pow(1.2, (jj+1))), 1. - 0.2* ii)- TMath::Pi()); } } for (int jj = 0; jj < ordersOfMag; jj++){ xList[lengthSteps][jj] = int(10 * pow(1.2, (jj+1))); yList[lengthSteps][jj] = fabs(alternative(int(10 * pow(1.2, (jj+1))))- TMath::Pi()); } TCanvas mycan; mycan.cd(); mycan.SetLogx(); mycan.SetLogy(); TGraph* myGraphArray [lengthSteps + 1]; for (int ii = 0; ii < lengthSteps + 1; ii++){ myGraphArray[ii] = new TGraph(ordersOfMag, xList[ii], yList[ii]); myGraphArray[ii]->SetLineColor(ii+1); myGraphArray[ii]->SetLineWidth(6); myGraphArray[ii]->SetMarkerStyle(ii); myGraphArray[ii]->SetMaximum(10); myGraphArray[ii]->SetMinimum(0.00001); if(ii ==0) { myGraphArray[ii]->Draw("AC*"); } else {myGraphArray[ii]->Draw("same"); } } mycan.SaveAs("Graph.root"); return 0; }