Python 3.7.3 (v3.7.3:ef4ec6ed12, Mar 25 2019, 16:52:21) 
[Clang 6.0 (clang-600.0.57)] on darwin
Type "help", "copyright", "credits" or "license()" for more information.
>>> import turtle, math
>>> alice = turtle.Turtle()
>>> def spiral(t, n, scale):
	for i in range(1, n+1):
		t.forward(math.sqrt(i)*scale)
		t.left(90)
		t.forward(1*scale)
		beta = math.atan2(math.sqrt(i),1)
		gamma = 180 - math.degrees(beta)
		t.left(gamma)
		t.forward(math.sqrt(i+1))
		t.left(180)
	return()

>>> def spiral(t, n, scale):
	for i in range(1, n+1):
		t.forward(math.sqrt(i)*scale)
		t.left(90)
		t.forward(1*scale)
		beta = math.atan2(math.sqrt(i),1)
		gamma = 180 - math.degrees(beta)
		t.left(gamma)
		t.forward(math.sqrt(i+1)*scale)
		t.left(180)
	return()

>>> alice.forward(10)
>>> alice.forward(50)
>>> alice.left(90)
>>> alice.forward(50)
>>> beta = math.atan2(math.sqrt(1),1)
>>> beta
0.7853981633974483
>>> gamma = 180 - math.degrees(beta)
>>> gamma
135.0
>>> alice.left(gamma)
>>> alice.forward(math.sqrt(2)*50)
>>> def spiral(t, n, scale):
	for i in range(1, n+1):
		t.forward(math.sqrt(i)*scale)
		t.left(90)
		t.forward(1*scale)
		beta = math.atan2(math.sqrt(i),1)
		gamma = 180 - math.degrees(beta)
		t.left(gamma)
		t.forward(math.sqrt(i+1)*scale)
		t.left(180)
	return()

>>> spiral(alice, 10, 50)
()
>>> alice.reset()
>>> spiral(alice, 10, 50)
()
>>> alice.reset()
>>> spiral(alice, 10, 20)
()
>>>