2322-The Pythagorean Theorem.sagews

html('<h2>The Pythagorean Theorem</h2>')
@interact
def pythagorean_triangle( \
        a = slider(1.0, 50.0, 0.5, 3.0), \
        b = slider(1.0, 50.0, 0.5, 4.0)) :
            
    point_a = [a, 0]
    point_b = [0, b]
    polygon = [[0, 0], point_a, point_b, [0, 0]]
    #p = polygon(t, rgbcolor=(1, 0, 0))
    triangle = line(polygon, rgbcolor=(1, 0, 0))

    a_text = "a=%s" % (n(a, digits=5), )
    a_show = text(a_text, (a/2 ,b/20), rgbcolor=(1,0,0))

    b_text = "b=%s" % (n(b, digits=5), )
    b_show = text(b_text, (a/5 ,0.7*b/2), rgbcolor=(1,0,0))

    c_text = "c=%s" % (n(sqrt(a^2 + b^2), digits=5), )
    c_show = text(c_text, (1.3*a/2 ,b/2), rgbcolor=(1,0,0))

    show(triangle + a_show + b_show + c_show, aspect_ratio=1)

The Pythagorean Theorem

html('<h2>The Euclidean Method for generating Pythagorean Triplets</h2>')
@interact
def pythagorean_triangle( \
        mm = input_box(default=2, label='Seed number 1', width=10), \
        nn = input_box(default=1, label='Seed number 2', width=10)) :

    try:
        mmm = float(mm)
        nnn = float(nn)
    except (ValueError, NameError, TypeError):
        print "cannot generate a triplet. Please enter valid numbers (1st number >= 2, and 2nd number >= 1"
        return

    a = mmm^2-nnn^2
    b = 2*mmm*nnn
    
    print "Based on the seed (%d, %d), the triplet is: (%d, %d, %d)" % (mmm, nnn, a, b, mmm^2+nnn^2, )
    
    point_a = [a, 0]
    point_b = [0, b]

    mm = '' # reset value for next time
    mmm = float() # generate 0.0
    
    polygon = [[0, 0], point_a, point_b, [0, 0]]
    #p = polygon(t, rgbcolor=(1, 0, 0))
    triangle = line(polygon, rgbcolor=(1, 0, 0))

    a_text = "a=%s" % (n(a, digits=5), )
    a_show = text(a_text, (a/2 ,b/20), rgbcolor=(1,0,0))

    b_text = "b=%s" % (n(b, digits=5), )
    b_show = text(b_text, (a/5 ,0.7*b/2), rgbcolor=(1,0,0))

    c_text = "c=%s" % (n(sqrt(a^2 + b^2), digits=5), )
    c_show = text(c_text, (1.3*a/2 ,b/2), rgbcolor=(1,0,0))

    show(triangle + a_show + b_show + c_show, aspect_ratio=1)

The Euclidean Method for generating Pythagorean Triplets

Seed number 1  Seed number 2  [removed] [removed] [removed] [removed]