Making a lamp
Doing the math
- Start with a square with corners A, B, C, D.
- Make E be the midpoint of AB, F the midpoint of CD, and G the midpoint of EF.
- Proportion EG using the golden ratio to find H, so that GH is the longer part.
- Proportion GF in the same way to find J.
- Draw line HK perpendicular to the face of square, and make its length = GH.
- Draw a similar line JL. KL is the ridge of the roof.
- Draw line HM, perpendicular to EF.
- Take the right triangle HKM, and solve for angle K.
- Make AB = 10, so EB = HM = 5 = k.
- If k = 5, then GR/5 = 1/m, so m = 3.09016994374948.
The golden ratio (GR:1) = 1/2(sqrt+1):1 = 1.61803398874989:1.
- k² + m² = h², so h = 5.87785252292473.
- Cosine(K) = m/h = 0.525731112119135, so K = 58.28 degrees
(the cosine of an angle = adjacent/hypotenuse).
- 2(K)= 116.56 or 116° 34' = the dihedral angle.