The activity that I propose in this post allows you to visualize the decimal figures of the number pi.
Lets start by the beginning.
Sounds familiar to you, right?
They are the first digits of the number pi (π) .
But, as you already know, the number pi does not end here, since it is an irrational number .
Irrational numbers are those that cannot be expressed as the quotient of two integers. That is, there are no two integers such that when divided by one another they result in the number pi.
Irrational numbers are characterized by having infinite decimal figures without any type of periodicity.
Notice. In August 2021, after more than 100 days of work, a team of Swiss scientists from the Center for Data Analysis, Visualization and Simulation at the Graubünden University of Applied Sciences managed to calculate 62.8 trillion digits of the number π.
The last ten currently known digits of the number π are 7817924264.
π, a number very present in our lives
The number pi indicates the relationship between the perimeter of a circle and its diameter . Its name comes precisely from the initial of the Greek word περιφέρεια (periphery). It has accompanied us from Antiquity to the present day, and continues to be one of the most important mathematical constants, present in multiple ways in our daily lives.
And maybe you will think that things don’t suit you… but nothing could be further from the truth! From the construction of spherical or circular objects, such as wheels, glasses, bottles, pipes or electrical cables to the operation of GPS, mobile phones or smart speakers, through endless applications in the Whether it is mathematics, physics or engineering, the number pi is part of your daily life, believe it or not.
International Pi Number Day
On March 14, International Pi Day is celebrated . And, precisely because of the importance of this number, it has also been chosen as the International Day of Mathematics .
But… why this day and not another?
Well, it turns out that, in Anglo-Saxon countries, March 14 is written 3/14 (yes, first the month -3- and then the day -14-), coinciding with the first three digits of said number: 3.14.
To celebrate this anniversary, I propose an activity that I saw for the first time here and that precisely allows you to highlight the non-periodicity of its infinite decimal figures.
It consists of drawing the “profile” of the number pi, as if it were the skyscrapers of a city.
You will need to:
– Decimal figures of the number pi
– Graph paper
At the end of the article you can download the free templates to carry out the activity.
– Place the squared paper horizontally.
– In the first column starting from the left, color 1 square, which corresponds to the first decimal figure of the number pi. In the second, 4. In the third, 1 again. And so on with the following decimal figures, one per column, until reaching the end of the page.
– If you want to represent the units (that is, the integer part of the number pi: 3), color 30 squares in the first column. 30 squares are equivalent to 30 tenths, which are 3 units. Then leave a blank space, corresponding to the comma, and continue with the decimal figures.
– You can assign a color to each number or paint them all black.
– Once you have finished, you can cut out the silhouette and paste it on a night sky, as seen in the photograph.
Now, take a look at the result. Doesn’t it remind you of the silhouette of a city (skyline)? Look at the height of the buildings. It doesn’t follow any pattern, so it’s impossible to predict how tall the next one will be.
Below I show you the “silhouette” of other irrational numbers that, like π, have infinite decimal figures that do not repeat following any period: the number e, the number φ (golden ratio) and root of 2.
root of 2
And now, in 3 dimensions
You can also represent the number pi in 3 dimensions, with rulers, polycubes or Lego pieces. You dare?
What did you think of this activity to visualize the decimal figures of the number pi?