[Paul Curtis] over at Segger has an interesting series of blog posts about calculating division. This used to be a hotter topic, but nowadays many computers or computer languages have support for multiplication and division built-in. But some processors lack the instructions and a library to do it might be less than ideal. Knowing how to roll your own might allow you to optimize for speed or space. The current installment covers using Newton’s algorithm to do division.
Steve Martin had a famous bit about how to be a millionaire and never pay taxes. He started out by saying, “First… get a million dollar. Then…” This method is a bit like that since you first have to know how to multiply before you can divide. The basic premise is twofold: Newton’s method let you refine an estimate of a reciprocal by successive multiplications and then multiplying a number a reciprocal is the same as dividing. In other words, if we need to divide 34 by 6, you could rewrite 34/6 to 34 * 1/6 and the answer is the same.
Continue reading “Apple Falling Division”
Newton’s Cradle was once upon a time, a popular desk toy in offices around the world. For [TecnoProfesor], however, it wasn’t quite flashy enough. Instead, they built a simulated version with flashing LEDs. As you do.
Rather than relying on the basic principles of the cradle to make it work, this relies on two servo motors to move the balls on the ends, with the ones in the middle remaining stationary. Each ball is fitted with an RGB LED, which flashes with the simulated “motion” of the cradle. By using ping pong balls, the light from the LEDs is nicely diffused. The frame is built from wooden dowels, metal rods, and acrylic.
It’s a project that is sure to confuse at first glance, but it’s a great way to learn basic microcontroller skills like interfacing with LEDs and servomotors. We’d love to see a version that works like a real Newton’s Cradle, flashing the LEDs as they are hit by their neighbours. We’ve even seen them automated, for the truly lazy among us. Alternatively, one could go completely ridiculous and have such a device tweet on every hit, though you might run afoul of the API’s spam restrictions. If you give it a go, drop us a line.
There’s a line from the original Star Trek where Khan says, “Improve a mechanical device and you may double productivity, but improve man and you gain a thousandfold.” Joan Horvath and Rich Cameron have the same idea about improving education, particularly autodidacticism or self-learning. They share what they’ve learned about acquiring an intuitive understanding of difficult math at the Hackaday Superconference and you can watch the newly published video below.
The start of this was the pair’s collaboration on a book about 3D printing science projects. Joan has a traditional education from MIT and Rich is a self-taught guy. This gave them a unique perspective from both sides of the street. They started looking at calculus — a subject that scares a lot of people but is really integral (no pun intended) to a lot of serious science and engineering.
You probably know that Newton and Leibniz struck on the fundamentals of calculus about the same time. The original papers, however, were decidedly different. Newton’s approach was more physical and less mathematical. Leibniz used formal logic and algebra. Although both share credit, the Leibniz notation won out and is what we use today.
Continue reading “Understanding Math Rather Than Merely Learning It”
The triangular frame of a traditional mountain bike needs to be the most rigid structure, and a triangle can be a very sturdy shape. So [Colin Furze] throws a spanner in the works, or, in this case, a bunch of springs. The video is below the break, but please try to imagine you are at a party, eyeballing some delicious salsa, yet instead of a tortilla chip, someone hands you a slab of gelatin dessert. The bike is kind of like that.
Anyone who has purchased springs knows there are a lot of options and terminology, such as Newton meters of force, extension, compression, and buckling. There is a learning curve to springs so a simple statement, for example “I want to make a bicycle of springs,” doesn’t have any easy answers. It is a lot like saying, “I want to make a microprocessor out of transistors“. This project starts with springs roughly the diameter of the old bike tubes, and it is a colossal failure. Try using cooked spaghetti noodles to make a bridge.
The first set of custom springs are not up to the task, but the third round produces something rideable. The result seems to be a ridiculous way to exercise your abs and is approximately a training unicycle mated with a boat anchor.
What makes this a hack? The video is as entertaining as anything [Colin] has made, but that does not make it a hack by itself. The hack is that someone asked a ridiculous question, possibly within reach of alcohol, and the answer came by building the stupid thing. A spring-bicycle could have been simulated six ways from Sunday on an old Android phone, but the adventure extracted was worth the cost of doing it in real life.
Continue reading “More Suspension Than Necessary”
Mathematics, as it is taught in schools, sometimes falls short in its mission to educate the pupils. This is the view of [Joan Horvath] and [Rich Cameron], particularly with respect to the teaching of calculus, which they feel has become a purely algebraic discipline that leaves many students in the cold when it comes to understanding the concepts behind it.
Their Hacker Calculus project aims to address this, by returning to [Isaac Newton]’s 1687 seminal work on the matter, Philosophiae Naturalis Principia Mathematica. They were struck by how much the Principia was a work of geometry rather than algebra, and they are seeking to return to [Newton]’s principles in a bid to make the subject more accessible to students left behind when it comes to derivatives and integrals. They intend to refine the geometric approach to create a series of practical items to explain the concepts, both through 3D printed items and through electronics.
We can see that this is an approach that has considerable merit, given that most Hackaday readers will have at some time or other sat through a maths lesson and come away wondering what on earth the teacher was talking about and having been baffled by further attempts to explain it through impenetrable maths-speak. If you were the kid who “got” calculus when the relationship between speed and acceleration – another thing we have [Newton] to thank for describing – was explained in your physics lessons, then you will probably understand.
The pair have some Hackaday Prize history, you may remember them from such previous entries as their 3D prints for the visually impaired project from last year.
Desk toys are perfect for when you don’t want to work. There’s a particularly old desk toy called the Newton’s cradle. If you don’t know the name, you’d still recognize the toy. It is some ball bearings suspended in midair on strings. If you pull back, say, two balls and let them swing to impact the other balls, the same number of balls on the other side will fly out. When they return, the same number will move on the other side and this repeats until friction wears it all down.
We think [JimRD] might be carried away on procrastination. You see, he not only has a Newton’s cradle, he has automated it with an Arduino. According to [Jim], this is his third attempt at doing so. You can see the current incarnation in the video, below.
Continue reading “Newton’s Cradle For Those Too Lazy To Procrastinate”