Why 41,25 stencil ?

michel123456 · May 25, 2018

Today I retrieved from a drawer this drawing instrument, called "stencil" or Schablon in German, that we used when drawing by hand (we stopped about twenty years ago).

Looking at it, I noticed this strange angle 41,25 degrees. Combined with the other one 7,10 degrees.

And I really could not recall why? What is so special with those 2 angles?

Internet came to the rescue and I found it, but just by curiosity, can you figure out what is so special with those 2 angles?

Edited May 25, 2018 by michel123456
adding images

**Strange** · May 25, 2018

Presumably for doing dimetric projection drawings: https://en.wikipedia.org/wiki/Axonometric_projection

Not sure why that specific angle though...

Sensei · May 25, 2018

Dimetric projection.

See "Engineer projection" in this article:

https://en.wikipedia.org/wiki/Axonometry

5b083d416de8a_DimetricProjection.png.6afa75a2ad2440c1cdf781348591fb3f.png

Edited May 25, 2018 by Sensei

**CharonY** · May 25, 2018

42/7 are the standard angles for dimetric projections, not sure about what is on there though. Also, it is a "Schablone" (with "e", though technically I should not complain about typos, if it was one).

Edit, just checked some drawings and it seems that there are variations in dimetric projections, including 41.25/7.11.

Edited May 25, 2018 by CharonY

michel123456 · May 27, 2018

Right. Sorry for the missing e in Schablone.

I couldn't figure the reason for those angles, but the German Wiki helped a bit.

Quote

Mathematischer Hintergrund:

Eine Ingenieur-Axonometrie entspricht einer senkrechten Parallelprojektion auf eine Ebene mit dem Normalenvektor (= negativer Projektionsrichtung) (7,1,1)⊤{\displaystyle ({\sqrt {7}},1{,}1)^{\top }} $({\sqrt {7}},1{,}1)^{\top }$ mit anschließender Skalierung um den Faktor 322≈1,06{\displaystyle {\tfrac {3}{2{\sqrt {2}}}}\approx 1{,}06} ${\tfrac {3}{2{\sqrt {2}}}}\approx 1{,}06$ . Der Grundriss des Normalenvektors schließt mit der x-Achse einen Winkel von arccos⁡(722)≈20,7∘{\displaystyle \arccos({\tfrac {\sqrt {7}}{2{\sqrt {2}}}})\approx 20{,}7^{\circ }} $\arccos({\tfrac {\sqrt {7}}{2{\sqrt {2}}}})\approx 20{,}7^{\circ }$ ein. Der Winkel gegenüber der x-y-Ebene beträgt arccos⁡(223)≈19,47∘{\displaystyle \arccos({\tfrac {2{\sqrt {2}}}{3}})\approx 19{,}47^{\circ }} $\arccos({\tfrac {2{\sqrt {2}}}{3}})\approx 19{,}47^{\circ }$ . Die exakten Winkel zwischen den Achsen sind:

α=arccos⁡(−74)≈131,4∘{\displaystyle \alpha =\arccos(-{\tfrac {\sqrt {7}}{4}})\approx 131{,}4^{\circ }} $\alpha =\arccos(-{\tfrac {\sqrt {7}}{4}})\approx 131{,}4^{\circ }$

β=arccos⁡(−18)≈97,18∘{\displaystyle \beta =\arccos(-{\tfrac {1}{8}})\approx 97{,}18^{\circ }} $\beta =\arccos(-{\tfrac {1}{8}})\approx 97{,}18^{\circ }$ .