EMS-US for the single use / 単体用EMS-US

These might be common pictures for you who have been watching my website.
Here I am showing the minimum profiled connection of the standard housings.
Most of the sizes of the standard housings are 2″(-inch), male or female, in common for the convenience of the users to make the most of the personal applications.
The default twisting angle is so clear to restore that you have only to make the entrance and exit openings intersect each other by the right angle.

If you have a bit more patience to read the closer explanation, I will show you the
amazing numeric secret of the EMS.
What is the right twisting angle of the EMS from the assumed starting position of one-dimensional connection of EMS of 120-deg deflection? Let’s assume the angle is “beta”.
Look at the diagram below.

You may know the ratio of the standard business paper is one by square root of two (1:1.4142….).
The angle “alpha” between the diagonal line and the long side is the same as the inclination of second light path of the EMS seen from behind.

And,2x-alpha = beta(70.5287…deg.)=the very twisting angle of the EMS!!
And cos(beta)=1/3. Isn’t it amazing???
And the ratio of 1:1.4142…. is called the “Silver Ratio”. Am I the only one who feel it so divine??

11/01 追記:EMSの数字的な神秘?について、以前より時々ご紹介していますが、皆さん、割りと無関心なようで、掲載する度に、正直、がっかりします。 まあ、「見えれば良い。」ということでしょうかね。^^; 確かに、EMSは原理を知らなくても使えますしね。 でも原理が理解できると、ずっと楽しさも増すんですけどね。^^;