Science and technology

Measure pi with a Raspberry Pi

March 14th is well known all over the world as Pi Day. Many individuals rejoice Pi Day by measuring pi with objects discovered round the home. I wished to do one thing related for this 12 months’s Pi Day utilizing my Raspberry Pi 3B. Read on to find out how I measured pi utilizing my Raspberry Pi.

What you may want:

  • Raspberry Pi single-board pc
  • Graph paper
  • Ruler with mm and cm measurements
  • Pen

1. Draw a circle

Pi is the ratio of the circumference of a circle to its diameter. To calculate pi, we have to measure each the circumference and diameter of a superbly drawn circle. Fortunately, the Raspberry Pi motherboard has mounting holes which might be sufficiently big to suit a pencil or pen. I caught a pin via one Pi board mounting gap, cautious to land the pin on the intersection of two strains on a chunk of graph paper.

Holding the pin nonetheless, I inserted a pen within the reverse mounting gap and drew a circle by transferring the pen across the pin. The solder factors on the underside of the Raspberry Pi motherboard can catch on the paper, however you possibly can draw circle in case you are cautious.

(Jim Hall, CC BY-SA 4.0)

2. Divide the circle into segments

Divide the circle in half by drawing a vertical line via the middle of the circle and once more into quarters by drawing a horizontal line via the circle. When I drew my circle, I positioned the pin precisely on the intersection of two strains on the graph paper, which makes discovering the vertical and horizontal heart strains straightforward to seek out. You can create an “eighth” slice by drawing a line throughout the diagonal.

(Jim Hall, CC BY-SA 4.0)

Further divisions are an train with the ruler. I used the ruler to seek out the midpoint of any two intersections of the “quarter-wedge” and the “one-eighth wedge” to make a 1/16 wedge. You can use the identical methodology to make smaller and smaller slices which might be 1/32 and 1/64 of a circle. By being very cautious, I used to be additionally in a position to measure a really slender wedge at 1/128 of a circle:

(Jim Hall, CC BY-SA 4.0)

3. Estimate the circumference

My smallest wedge is 1/128 of a circle. With such a small slice, the outer arc of the wedge is so small that we will approximate it with a straight line. This won’t really be 1/128 of the circle’s circumference, however will probably be shut sufficient that we will use it as estimate.

(Jim Hall, CC BY-SA 4.0)

Using the mm measurement on my ruler, I measured the outer arc of my 1/128 wedge at 3.8mm. With that, I can estimate the circumference of my circle as 3.8mm occasions 128, or 486.4mm. To convert to centimeters, divide by ten: 48.64cm.

4. Calculate pi

The worth of pi is the ratio of the circumference of a circle to its diameter. We estimated the circumference in step 3. Measuring the diameter is a straightforward train of utilizing the ruler to measure throughout the circle. My circle is 15.4cm.

Now that we all know the circumference and diameter, we will calculate pi as 48.64 divided by 15.4, which is 3.158. That’s not too far off from the precise worth of pi, at 3.141.

Measuring pi is a enjoyable math train! Math followers of all ages can use easy instruments comparable to graph paper, pen, and ruler to measure pi on their very own. Use your Raspberry Pi in a enjoyable, new method to attract a circle and measure pi independently. This is an estimate since we’re approximating a 1/128 arc on a circle as a straight line, however this will get us shut sufficient with out an excessive amount of effort.

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