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
Math
536 Puzzles: Problem & Solution #1: Concerning a Check
A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?
- The first sheet uses a brute force method of stepping through all the values from 00.00 to 99.99 and looking for an integer solution
- The second sheet uses the relation below to drive towards a less brute force method
- The third sheet of the spread sheet shows how the solution is periodic like a set of gears. The constant term added is represented as the column offset number and is analogous to a number of teeth offset from zero position at the start of turning of the gears.
- The fourth sheet uses 5 and 7 to simplify the problem