When you transform f(x)=e^x 1 unit to the left, you’re left with g(x)=e^(x+1) (Fig. A). This transformation is pretty simple; the new line is 1 unit away. However, it’s only 1 unit away horizontally. Vertically, it varies depending on the x value. The vertical difference at x=-1 is a lot smaller than the vertical difference at x=1. On this recent #hack-night, @carrot and I set out to transform f(x) so that at any point along f(x), the distance to the closest point on g(x) is equal to 1. Essentially, g(x) is 1 unit away throughout, not horizontally (Fig. B). This proved to be quite difficult. There were a lot of quadratics that needed solving, and we also had to use the pythagorean theorem to get some distances. He can probably explain the math behind it a lot better than I can. Anyways, here are a few links if you want to try it out: • Exponential Functions - • Quadratic Functions - • Linear Functions - • Circles - (I think)
desmos-threat emoji
math-is-math emoji
while I wait for xcode to do an install, I will share a fun fact @carrot taught me about logic gates recently :and: you only need the NAND gate (AND gate followed by NOT) to do every single possible logic operation ever. that means that every possible logic circuit can be made to use only NAND! in fact, a physical NAND transistor takes up less area than an AND transistor. to make an AND, you’d actually make a NAND and then invert the output.
firming up a metaphor about RAM and CPU registers.. thank you @carrot for helping me 📫 ✉️