Humanity pretty much has Pi figured out at this point. We’ve calculated it many times over and are confident about what it is down to many, many decimal places. However, if you fancy estimating it with some electronic assistance, you might find this project from [Roni Bandini] interesting.

[Roni] programmed an Arduino Nano R4 to estimate Pi using the Monte Carlo method. For this specific case, it involves drawing a circle inscribed inside a square. Points are then randomly scattered inside the square, and checked to see if they lie inside or outside the circle based on their position and distance of the circle’s outline from the center point of the square. By taking the ratio of the points inside the circle to the total number of points, you get an approximation of the ratio of the square and circle’s areas, which is equal to Pi/4. Thus, multiply the ratio by 4, and you’ve got your approximation of Pi.

[Roni] coded a program to run the Monte Carlo simulation on the Arduino Nano R4, taking advantage of the mathematical benefits of its onboard Floating Point Unit. It generates 100 new samples for the Monte Carlo approximation every second, improving the estimation of pi as it goes. It then displays the result on a 7-segment display, and beeps as it goes. [Roni] readily admits the project is a little too close in appearance to a classic Hollywood bomb.

We’ve seen some other neat Pi-calculating projects before, too.

Trigonometry is a struggle for some students. Perhaps one of the reasons for this is that instruction can be something of a one-way street, and concepts can be hard to grasp until more technical building blocks are learned. 

As seen here, researchers at the Universidad del Desarrollo in Chile aim to change that with a trigonometry tabletop display called TAMI, or Tangible Mathematics Interface. This nearly horizontal screen shows mathematical relationships, while allowing students to interact with them using physical controls. 

The most prominent controller here is a large rotary wheel. Students rotate this to modify the angle shown in the middle, and observe how concepts like sine and cosine react to this manipulation. An Arduino Leonardo takes input from this and other controls, and passes it along to a computer. This then handles on-screen info and even plays sounds as needed!

Makers need to familiarize themselves with the core concepts and the theory involved in creating applications such as Motion Sensing and Face Tracking. As the technology is churning out new hardware day and night, DIYers need to work hard to keep up and always be in touch with the latest technology around them.

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For example, anyone working with Accelerometers/ Gyroscopes or Inertial Measurement Units needs to understand the theory of Vectors, Force, Gravity and be able to work out complex mathematical problems. They may easily get an Arduino Board and an Accelerometer Breakout or an IMU Board and use a library instead of writing their own code but to truly understand the theory behind it; how the device actually works, is not for the faint of heart.

One such problem is the Face Tracking Application. Unless you know the real theory behind how the Algorithm actually works, you can only wonder about that robot which follows its master. Greg Borenstein had an idea of creating a website dedicated to this issue. Makematics – Math for Makers.

In an introductory post, Greg writes:

” I hope to show that a normal programmer with no special academic training can grapple with these areas of research and find a way in to understanding them. And as I go I aim to create material that will help others do the same. If I can do it, there’s no reason you can’t.”

More and more people should step forward and create or compile a good amount of research data to help fellow makers and DIYers in solving complex mathematical problems.