Math
Eulers Theorem
If you followed the proof for Fermat's little theorem then you can understand this generalization rapidly. As before when the integer a is coprime to p you get the jumble of all the integers 1,2,3…p-1. This was guaranteed by p being prime in Fermat's little theorem. When you relent on that condition then you have some integers a that are not coprime to p and they will not give you a full contingent of integers. See the spread sheet clips below
2 is coprime to 15 and thus all values 0 through 14 are cycled through. 3 is not coprime to 15 and thus the gearing does not cycle through all values.
Math
Euler Fermat Theorem – Fermats Little Theorem
Research Links
- Fermat–Euler theorem
- Euler's totient function
- Fermat's little theorem
- Proofs of Fermat's little theorem
- Proof of Fermat's Little Theorem
- Chinese remainder theorem
- Eulers Theorem – a more general version that only specifies coprime requirement instead of prime requirement.
Architecture
Sawhorse Plans
Research Links
- Sawhorse plans – video here
Materials
- Quantity=3: 10-ft. 2×4's. Spreadsheet if you want to modify lengths.
- Quantity=36: 3-in. wood screws
- SpreadSheet for Brazil where Sul Para supplies 3 meter long 2x4s – They are really 5cm x 10 cm
- SpreadSheet for USA 10 Feet long 2×4
Steps
- Assemble the three boards that make up the I-beam.
- Attach the legs, using a framing square to square the legs to the beam.
- Attach the rails last. – Do not take the height above ground level of the rails literally. Depending on the dimensions of your 2x4s this can vary. Proceed by attaching the short rails where they fit best against the legs. then position the long rails to match. My spreadsheets change dimensions in order to minimize waste. Each
Buy Links
- MercadoLivre: parafuso madeira 5 x 80mm
- MercadoLivre: Parafuso Madeira Chipboard Phillips 5 X 80 Mm Cx 200 Peças
The following photos show the results obtained with the following spreadsheet's design
- Table SawHorses – units in centimeter
