Why NASA Only Needs Pi To So Many Decimal Places

December 17, 2024 by Lewin Day 39 Comments

If you’re new to the world of circular math, you might be content with referring to pi as 3.14. If you’re getting a little more busy with geometry, science, or engineering, you might have tacked on a few extra decimal places in your usual calculations. But what about the big dogs? How many decimal places do NASA use?

*NASA doesn’t need this many digits. It’s likely you don’t either. Image credits: NASA/JPL-Caltech*

Thankfully, the US space agency has been kind enough to answer that question. For the highest precision calculations, which are used for interplanetary navigation, NASA uses 3.141592653589793 — that’s fifteen decimal places.

The reason why is quite simple, going into any greater precision is unnecessary. The article demonstrates this by calculating the circumference of a circle with a radius equal to the distance between Earth and our most distant spacecraft, Voyager 1. Using the formula C=2pir with fifteen decimal places of pi, you’d only be off on the true circumference of the circle by a centimeter or so. On solar scales, there’s no need to go further.

Ultimately, though, you can calculate pi to a much greater precision. We’ve seen it done to 10 trillion digits, an effort which flirts with the latest Marvel movies for the title of pure irrelevance. If you’ve done it better or faster, don’t hesitate to let us know!

Print Yourself Penrose Wave Tiles As An Excellent Conversation Starter

October 1, 2024 by Lewin Day 15 Comments

Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up repeating on some scale or other. That is, unless you go with something like a Penrose Wave Tile. Discovered by mathematician Roger Penrose, they never exactly repeat, no matter how you lay them out.

[carterhoefling14] decided to try and create Penrose tiles at home—with a 3D printer being the perfect route to do it. Creating the tiles was simple—the first step was to find a Penrose pattern image online, which could then be used as the basis to design the 3D part in Fusion 360. From there, the parts were also given an inner wave structure to add further visual interest. The tiles were then printed to create a real-world Penrose tile form.

You could certainly use these Penrose tiles as decor, though we’d make some recommendations if you’re going that path. For one, you’ll want to print them in a way that optimizes for surface quality, as post-processing is time consuming and laborious. If you’re printing in plastic, probably don’t bother using these as floor tiles, as they won’t hold up. Wall tiles, though? Go nuts, just not as a splashback or anything. Keep it decorative only.

You can learn plenty more about Penrose tiling if you please. We do love a bit of maths around these parts, too. If you’ve been making your own topological creation, don’t hesitate to drop us a line.

Office Supplies Make Math Sculptures If You Know What You’re Doing

July 17, 2024 by Lewin Day 7 Comments

Ever been fiddling around at your desk in the office, wondering if some grander structure might come from an assemblage of paper clips, pens, and binder clips? You’re not alone. Let your mind contemplate these beautiful maths sculptures from [Zachary Abel].

[Zachary] has a knack for both three-dimensional forms and the artistic use of color. His Möbius Clips sculpture ably takes 110 humble pieces of office equipment in multiple colors, and laces them into a continuous strip that has beguiled humanity for generations. The simple paper clip becomes a dodecahedron, a colorful spiralling ball, or a tightly-stitched box. He does great things with playing cards too.

What elevates his work is that there’s a mathematical structure to it. It’s so much more than a pile of stationary, there’s always a geometry, a pattern which your mind latches on to when you see it. He also often shares the mathematical background behind his work, too.

If you’re fumbling about with the contents of your desk drawer while another Zoom meeting drags on, you might want to challenge yourself to draw from [Zachary’s] example. If you pull off something fantastical, do let us know!

Making Art With Maxwell’s Equations

July 17, 2024 by Lewin Day 5 Comments

When you think of art, you might think of portraiture, landscapes, or other kinds of paintings. But mathematics can feel artistic at times, too. We’ve all seen gorgeous Mandelbrot fractals, and less gorgeous Julia fractals, but that’s not all that’s out there. As [Prof. Halim Boutayeb] demonstrates, Maxwell’s equations can show us some real beauty, too.

The work involves running simulations of multiple electromagnetic sources moving, bouncing around, interacting, and so on. The art comes in the plotting of the fields, in warm colors or just outright rainbows. The professor does a great job of pairing some of these videos with pumping electronic music, which only adds to the fun.

Of course, the colors are pretty, but there’s a lot of valuable physics going on behind all this. Thankfully, there are all kinds of additional resources linked for those eager to learn about the Finite Difference Time Domain method and how it can be used for valid simulation tasks.

Throw this kind of stuff on a projector at your next rave and you will not be disappointed. Video after the break.

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Organic Fibonacci Clock Is All About The Spiral

January 12, 2023 by Lewin Day 5 Comments

Whether you’re a fan of compelling Tool songs, or merely appreciate mathematical beauty, you might be into the spirals defined by the Fibonacci sequence. [RuddK5] used the Fibonacci curve as the inspiration for this fun clock build.

The intention of the clock is not to display the exact time, but to give a more organic feel of time, via a rough representation of minutes and hours. A strip of addressable LEDs is charged with display duty. The description is vague, but it appears that the 24 LEDs light up over time to show the amount of the day that has already passed by. The LEDs are wound up in the shape of a Fibonacci spiral with the help of a 3D printed case, and is run via a Wemos D1 microcontroller board.

It’s a fun build, and one that we can imagine would scale beautifully into a larger wall-hanging clock design if so desired. It at once could display the time, without making it immediately obvious, gradually shifting the lighting display as the day goes on.

We’ve seen other clocks rely on the mathematics of Fibonacci before, too. If you’ve cooked up your own fun clock build, don’t hesitate to let us know!

How To Hide A Photo In A Photo

May 1, 2022 by Jenny List 32 Comments

If you’ve ever read up on the basics of cryptography, you’ll be aware of steganography, the practice of hiding something inside something else. It’s a process that works with digital photographs and is the subject of an article by [Aryan Ebrahimpour]. It describes the process at a high level that’s easy to understand for non-maths-wizards. We’re sure Hackaday readers have plenty of their own ideas after reading it.

The process relies on the eye’s inability to see small changes at the LSB level to each pixel. In short, small changes in colour or brightness across an image are imperceptible to the naked eye but readable from the raw file with no problems. Thus the bits of a smaller bitmap can be placed in the LSB of each byte in a larger one, and the viewer is none the wiser.

We’re guessing that the increased noise in the image data would be detectable through mathematical analysis, but this should be enough to provide some fun. If you’d like a closer look, there’s even some code to play with. Meanwhile as we’re on the topic, this isn’t the first time Hackaday have touched on steganography.

Genaille’s Rods: When Paint Sticks Do Math

April 26, 2022 by Ryan Flowers 2 Comments

What is a hacker, if not somebody who comes up with solutions that other just don’t see? All the pieces may be in place, but it takes that one special person to view the pieces as greater than the sum of their parts. As [Chris Staecker] explains in the video below the break, Henri Genaille was one such person.

When French mathematician Edouard Lucas (himself well known for calculating the longest prime number found by hand) posed a mathematical problem at the French Academy, a French railway engineer named Henri Genaille developed the rods we’re discussing now.

Genaille’s Rods are designed to perform multiplication. But rather than require computation by the user, the rods would simply need to be laid out in the correct order. The solution could readily be found by just following the lines in the correct pattern. This might sound a lot like cheating, and that’s exactly what it is. No manual math needed to be done. Genaille also created rods for doing long division, which we’re sure were every bit as enthralling as the multiplication rods. Demonstrations of both are included in the video below.

While Genaille’s Rods have gone the way of the slide rule, we can’t help but wonder how many engineers and scientists carried around a set of marked up wooden sticks in their pocket protector.

If designing and building manual mathematical machines is something that you think really adds up to a good time, check out this post on how to design and build your own circular slide rule!

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