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Exploring Exercise 2.39 in "Math for Programmers" by P. Orland
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| ''' | |
| Created on Jun 3, 2023 | |
| @author: prhodes | |
| ''' | |
| from ch02.vector_drawing import * | |
| from math import sqrt, pi, cos, sin, tan, asin, acos, atan, atan2, isclose | |
| def main(): | |
| print( "Hello, Exercise 2.39\n" ) | |
| # Assignment: | |
| # Find another point in the plane with the same tangent as | |
| # theta, namely -3/2. Use Python's implementation of arctangent | |
| # math.atan, to find the value of this angle | |
| print( "atan(-3/2): ", atan(-3/2), ", in degrees: ", rads_to_degrees(atan(-3/2) ), "\n" ) | |
| print( "tan(-0.982793723247329): ", tan(-0.982793723247329), "\n" ) | |
| polar_23 = cart_to_polar( (2,-3) ) | |
| angle_23 = polar_23[1] | |
| print( "Angle_23: ", angle_23, "\n" ) | |
| print( "Angle_23 in rads: ", degrees_to_rads( angle_23 ), "\n" ) | |
| print( "tan(", angle_23, "): ", tan(angle_23), "\n" ) | |
| print( "tan(", degrees_to_rads(angle_23), "): ", tan(degrees_to_rads(angle_23)), "\n" ) | |
| points = [] | |
| for x in range( -5, 6 ): | |
| for y in range( -5, 6 ): | |
| polar = cart_to_polar( (x,y ) ) | |
| angle = degrees_to_rads( polar[1] ) | |
| if( x == 2 and y == -3 ): | |
| print( "angle: ", angle, "\n" ) | |
| if( isclose( angle, atan(-3/2), abs_tol=0.01) ): | |
| print( "OK" ) | |
| points.append( (x,y) ) | |
| print( "Points: ", points, "\n" ) | |
| def degrees_to_rads( degrees ): | |
| # 1° × π/180 = 0.01745rad | |
| rads = degrees * (pi/180) | |
| return rads | |
| def rads_to_degrees( rads ): | |
| # 1rad × 180/π = 57.296° | |
| degrees = rads * (180/pi) | |
| return degrees | |
| def cart_to_polar( cart ): | |
| x, y = cart[0], cart[1] | |
| angle = atan2( y, x ) | |
| return ( length(cart), angle * (180/pi) ) | |
| def polar_to_cart( polar ): | |
| distance = polar[0] | |
| angle_degrees = polar[1] | |
| print( "angle_degrees: ", angle_degrees, "\n" ) | |
| angle_rads = angle_degrees * ( pi / 180 ) | |
| print( "distance: ", distance, "\n" ) | |
| print( "angle_rads: ", angle_rads, "\n" ) | |
| cos_angle = cos(angle_rads) | |
| sin_angle = sin(angle_rads) | |
| print( "cos_angle: ", cos_angle, "\n" ) | |
| print( "sin_angle: ", sin_angle, "\n" ) | |
| x = cos_angle * distance | |
| y = sin_angle * distance | |
| print( "x: ", x, "\n" ) | |
| print( "y: ", y, "\n" ) | |
| return (x,y) | |
| def perimeter( vectors ): | |
| num_items = len( vectors ) | |
| perimeter = 0 | |
| for i in range( 0, num_items ): | |
| print( i, "\n" ) | |
| if( i == (num_items -1 )): | |
| perimeter = perimeter + (distance( vectors[num_items-1], vectors[0])) | |
| else: | |
| perimeter = perimeter + (distance(vectors[i], vectors[i+1])) | |
| return perimeter | |
| def distance( v1, v2 ): | |
| displacement = subtract( v1, v2 ) | |
| distance = sqrt( (displacement[0]**2) + (displacement[1]**2 ) ) | |
| return distance | |
| def translate( translation, vectors ): | |
| # a "one liner" version | |
| return [ add(translation,v) for v in vectors ] | |
| def subtract( v1, v2 ): | |
| return ( v1[0] - v2[0], v1[1] - v2[1] ) | |
| def add( v1, v2 ): | |
| return ( v1[0] + v2[0], v1[1] + v2[1] ) | |
| def scale( v, scalar ): | |
| return (v[0]*scalar, v[1]*scalar) | |
| def length( v ): | |
| return sqrt( v[0]**2 + v[1]**2 ) | |
| if __name__ == '__main__': | |
| main() |
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