With none of the major leagues in any team sport currently meeting, sports fans have a huge void that has to be filled with something. For [Shane Wighton], the machine shop is the place to go when sports let you down, and the result is this basketball backboard that lets you sink every shot every time.
When we first saw this, we thought for sure it would be some overly complicated motorized affair that would move the hoop to catch the basketball, sort of like the dart-catching dartboard we featured some time ago. And while that would be awesome and somebody should totally build that so we can write it up, [Shane]’s hoop dream is a lot simpler mechanically, even if the math needed to determine the proper shape for the backboard was complex. He wrote software to simulate throws from hundreds of positions to determine the shape for the board, which ends up looking like a shallow elliptic paraboloid. The software created a mesh that was translated into CNC tool paths in Fusion 360, and the backboard was carved from blocks of softwood.
The first tests were disappointing; instead of landing every shot, the board seemed to be actively denying them. [Shane] had to puzzle over that for a while before realizing that he didn’t account for the radius of the ball, which means the centroid never actually contacts the backboard. Rather than recalculate and create a new backboard, he just shifted the hoop out from the backboard by a ball radius. With that expedient in place, the setup performed exactly as calculated.
[Shane] may have taken the long road to hoops glory, but we appreciate the effort and the math lesson. And the fact that this ends up being the same shape as some antennas is a plus.
Continue reading “A Basketball Hoop That Never Lets You Brick”
Today is March 14th, or Pi Day because 3.14 is March 14th rendered in
month.day date format. A very slightly better way to celebrate the ratio of a circle’s circumference to its diameter is July 22nd, or 22/7 written in
day/month order, a fractional approximation of pi that’s been used for thousands of years and is a better fit than 3.14. Celebrating Pi Day on July 22nd also has the advantage of eschewing middle-endian date formatting.
But Pi Day is completely wrong. We should be celebrating Tau Day, to celebrate the ratio of the circumference to the radius instead of the diameter. That’s June 28th, or 6.283185…. Nonetheless, today is Pi Day and in the absence of something truly new and insightful — we’re still waiting for someone to implement a spigot algorithm in 6502 assembly, by the way — this is a fantastic opportunity to discuss something tangentially related to pi, the history of mathematics, and the idea that human knowledge builds upon itself in an immense genealogy stretching back to the beginning of history.
This is our Pi Day article, but instead of complaining about date formats, or Tau, we’re going to do something different. This is how you approximate pi with the Monte Carlo method, and how anyone who can count to a million can get a better approximation of one the fundamental constants of the Universe than Archimedes.
Continue reading “Archimedes Would Have Known Better If He Could Count To A Million”
Ever wish you could guess more precisely? Or maybe just make your guesses look confusingly legitimate? Guesstimate could help.
It uses Monte Carlo simulations to add some legitimacy to the ranges given to it. For example, if you say the cost of lumber for your next project could be between 2 and 8 dollars a piece, you don’t typically mean that it’s equally likely to be any of those numbers. Most people mean that the boards are most likely to be around 3-5 dollars and everything lower or higher is less probable. Using different shaped distributions, Guesstimate can help include this discrepancy of thought into your pseudo-calculations.
It’s a neat bit of code with a nice interface. There is a commercial side to the project for those who want to collaborate openly or pay someone to host it privately. It has a few neat example models for those interested.
Does anyone use anything like this in their daily lives? Is there another similar project out there? This kind of thing is pretty cool!