Integer triangle formula_112 and formula_113 generate the same triple. Unfortunately the two pairs can both be of gcd=3, so we can't avoid duplicates by simply skipping that case. Instead, duplicates can be avoided by formula_27 going only till formula_115. Note that we still need to divide by 3 if gcd=3. The only solution for formula_116 under the above constraints is formula_117 for formula_118. With this additional formula_119 constraint all triples can be generated uniquely. An Eisenstein triple is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 degrees. Integer triangles
Helix angle triangle, and calculating the angle that is formed. Note that while the terminology directly refers to screws, these concepts are analogous to most mechanical applications of the helix angle. The helix angle can be expressed as: where The helix angle is crucial in mechanical engineering applications that involve power transfer and motion conversion. Some examples are outlined below, though its use is much more widely spread. Cutting a single helical groove into a screw-stock cylinder yields what is referred to as a single-thread screw. Similarly, one may construct a double-thread screw provided that the helix angle is the same, and