various fixes in interacts

src/sage/interacts/library.py

@@ -418,7 +418,7 @@ def distance(x1_y1, x2_y2):
     # are adjacent and the side c is opposite to the angle
     def angle(a, b, c):
         a,b,c = map(float,[a,b,c])
-        return acos((b**2 + c**2 - a**2)/(2*b*c))
+        return acos(0.5 * (b**2 + c**2 - a**2) / (b * c))
 
     # Returns the area of a triangle when an angle alpha
     # and adjacent sides a and b are known
@@ -454,14 +454,10 @@ def area(alpha, a, b):
     labels = a_label + b_label + c_label
 
     show(unit_circle + triangle + triangle_points + labels, figsize=[5, 5], xmin=-1, xmax=1, ymin=-1, ymax=1)
-    angl_txt = r"$\angle A = {%s}^{\circ},$ $\angle B = {%s}^{\circ},$ $\angle C = {%s}^{\circ}$" % (
-            math.degrees(ak[0]),
-            math.degrees(ak[1]),
-            math.degrees(ak[2])
-        )
-    html(angl_txt)
-    html(r"$AB = %s,$  $BC = %s,$  $CA = %s$"%(al[2], al[0], al[1]))
-    html(r"Area of triangle $ABC = %s$"%A)
+    html(r"$\angle A = {%.3f}^{\circ},$ $\angle B = {%.3f}^{\circ},$ $\angle C = {%.3f}^{\circ}$"
+         % (math.degrees(ak[0]), math.degrees(ak[1]), math.degrees(ak[2])))
+    html(r"$AB = %.6f$, $BC = %.6f$, $CA = %.6f$" % (al[2], al[0], al[1]))
+    html(r"Area of triangle $ABC = %.6f$" % A)
 
 @library_interact
 def unit_circle(
@@ -1595,12 +1591,12 @@ def polar_prime_spiral(
             t = SR.var('t')
             a=1.0
             b=0.0
-            if n > (floor(sqrt(n)))**2 and n <= (floor(sqrt(n)))**2 + floor(sqrt(n)):
-                c = -((floor(sqrt(n)))**2 - n)
-                c2= -((floor(sqrt(n)))**2 + floor(sqrt(n)) - n)
+            S = int(sqrt(n))
+            if n <= S * (S + 1):
+                c = n - S**2
             else:
-                c = -((ceil(sqrt(n)))**2 - n)
-                c2= -((floor(sqrt(n)))**2 + floor(sqrt(n)) - n)
+                c = n - (S + 1)**2
+            c2 = n - S * (S + 1)
             html('Pink Curve:  $n^2 + %s$' % c)
             html('Green Curve: $n^2 + n + %s$' % c2)
             m = SR.var('m')

src/sage/interacts/test_jupyter.rst

@@ -47,8 +47,8 @@ Test all interacts from the Sage interact library::
       dpi: IntSlider(value=100, description=u'dpi', max=300, min=10, step=10)
     <h2>Polar Prime Spiral</h2>           <div style="white-space: normal;">          For more information about the factors in the spiral, visit           <a href="http://www.dcs.gla.ac.uk/~jhw/spirals/index.html" target="_blank">          Number Spirals by John Williamson</a>.</div>
     <script type="math/tex">n = 89</script>
-    Pink Curve:  <script type="math/tex">n^2 + 8.0</script>
-    Green Curve: <script type="math/tex">n^2 + n + -1.0</script>
+    Pink Curve:  <script type="math/tex">n^2 + 8</script>
+    Green Curve: <script type="math/tex">n^2 + n + -1</script>
 
     sage: test(interacts.calculus.taylor_polynomial)
     Interactive function <function taylor_polynomial at ...> with 3 widgets
@@ -103,16 +103,6 @@ Test all interacts from the Sage interact library::
     <script type="math/tex">Ax^2 + Bx + C = 0</script>
     <script type="math/tex">x = \frac{-B\pm\sqrt{B^2-4AC}}{2A} = \frac{-1\pm\sqrt{1^2-4*1*-2}}{2*1} = \frac{-1\pm\sqrt{\color{Green}{9}}}{2} = \begin{cases}1\\-2\end{cases}</script>
 
-    sage: test(interacts.calculus.trigonometric_properties_triangle)
-    Interactive function <function trigonometric_properties_triangle at ...> with 3 widgets
-      a0: IntSlider(value=30, description=u'A', max=360)
-      a1: IntSlider(value=180, description=u'B', max=360)
-      a2: IntSlider(value=300, description=u'C', max=360)
-    <h2>Trigonometric Properties of a Triangle</h2>
-    <script type="math/tex">\angle A = {60.0}^{\circ},</script> <script type="math/tex">\angle B = {45.0}^{\circ},</script> <script type="math/tex">\angle C = {75.0}^{\circ}</script>
-    <script type="math/tex">AB = 1.93185165258,</script>  <script type="math/tex">BC = 1.73205080757,</script>  <script type="math/tex">CA = 1.41421356237</script>
-    Area of triangle <script type="math/tex">ABC = 1.18301270189</script>
-
     sage: test(interacts.calculus.secant_method)
     Interactive function <function secant_method at ...> with 5 widgets
       title: HTMLText(value=u'<h2>Secant method for numerical root finding</h2>')
@@ -270,9 +260,9 @@ Test all interacts from the Sage interact library::
       a1: IntSlider(value=180, description=u'B', max=360)
       a2: IntSlider(value=300, description=u'C', max=360)
     <h2>Trigonometric Properties of a Triangle</h2>
-    <script type="math/tex">\angle A = {60.0}^{\circ},</script> <script type="math/tex">\angle B = {45.0}^{\circ},</script> <script type="math/tex">\angle C = {75.0}^{\circ}</script>
-    <script type="math/tex">AB = 1.93185165258,</script>  <script type="math/tex">BC = 1.73205080757,</script>  <script type="math/tex">CA = 1.41421356237</script>
-    Area of triangle <script type="math/tex">ABC = 1.18301270189</script>
+    <script type="math/tex">\angle A = {60.000}^{\circ},</script> <script type="math/tex">\angle B = {45.000}^{\circ},</script> <script type="math/tex">\angle C = {75.000}^{\circ}</script>
+    <script type="math/tex">AB = 1.931852</script>, <script type="math/tex">BC = 1.732051</script>, <script type="math/tex">CA = 1.414214</script>
+    Area of triangle <script type="math/tex">ABC = 1.183013</script>
 
     sage: test(interacts.geometry.special_points)
     Interactive function <function special_points at ...> with 10 widgets