//////////////////// // // Name: Pie in Physics #PiDay // Author: Shadow // Version: 1.0.3 // Date: 14.03.2019 // Description: PI approximation involving physics. // Imagine two circles on the x-axis, // the first standing still with a mass // of 1, the second one moving left with // a mass of 100^x. On the left side, // there is placed a wall which lets // a circle bounce back. // Furthermore, let us assume there is // no friction and the collisions // are elastic, meaning no energy and // therefore no speed is lost. // => v1 + u1 = v2 + u2 // Under these circumstances, we count // the number of collisions between the // left circle both with the wall and // the right circle. // The result is... surprising. // Input: The amount of digits of PI you want to // calculate. // Planned: Performance improvements maybe, but I'd // need suggestions for that. // The code runs smoother on the web version. // Reference: I linked the sources in the comments. // //////////////////// // //////////PREPROCESSOR////////// // #include #include // //////////CLASSES////////// // struct Element { const double m_Radius; double m_x; double m_mass; double m_velocity; static unsigned int m_collisions; Element(); Element( double, double, double ); inline void move() { m_x += m_velocity; if ( m_x <= 0 ) { ++Element::m_collisions; m_x = 0.0; m_velocity = -m_velocity; } } }; Element::Element() : m_Radius{ 2.0 }, m_x{ 0.0 }, m_mass{ 0.0 }, m_velocity{ 0.0 } {} Element::Element( double x, double m, double v ) : m_Radius{ 2.0 }, m_x{ x }, m_mass{ m }, m_velocity{ v } {} unsigned int Element::m_collisions = 0; // //////////FUNCTIONS////////// // bool checkCollision( const Element& e1, const Element& e2 ) { return ( e2.m_x - e1.m_x ) <= ( e1.m_Radius + e2.m_Radius ); } void applyElasticCollision( Element& e1, Element& e2 ) { ++Element::m_collisions; double u1; double u2; u1 = ( ( e1.m_mass - e2.m_mass ) * e1.m_velocity + 2 * e2.m_mass * e2.m_velocity ) / ( e1.m_mass + e2.m_mass ); u2 = ( ( e2.m_mass - e1.m_mass ) * e2.m_velocity + 2 * e1.m_mass * e1.m_velocity ) / ( e1.m_mass + e2.m_mass ); e1.m_velocity = u1; e2.m_velocity = u2; } // //////////MAIN FUNCTION////////// // int main() { unsigned int exponent { 0 }; std::cout << "Please enter the amount of decimal places of PI you want to calculate: "; std::cin >> exponent; std::cout << exponent << std::endl; unsigned int& accuracy { exponent }; Element e1{ 4.0, 1.0, 0.0 }; Element e2{ 10.0, std::pow( 100.0, exponent ), -( 1 / std::pow( 10.0, accuracy ) ) }; while ( e1.m_velocity < 0 || e2.m_velocity < 0 || e1.m_velocity > e2.m_velocity ) { e1.move(); e2.move(); if ( checkCollision( e1, e2 ) ) { applyElasticCollision( e1, e2 ); } if ( e2.m_x <= e1.m_x ) { std::cout << "\n\nInfinite Loop detected. Terminating..."; break; } } std::cout << "\nTotal number of collisions: " << Element::m_collisions << std::endl; return 0; }