Enjoy a slice of Pi Day

Pi day is here once again on March 14, 3/14 and I have scoured various interesting articles for engineers regarding this mathematical number.

When I first heard of Pi in grammar school, it was presented to us in class as 22/7, a seemingly ordinary ratio of two numbers. Little did I know back then how important it would be to my career as an engineer.

The Greek symbol Pi, π , has been the source of many articles over the years. Steven Bogart, a mathematics instructor at Georgia Perimeter College, wrote an article in Scientific American entitled What is Pi, and how did it originate?. In his article Professor Bogart states the following:

According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery, and became standard mathematical notation roughly 30 years later.

NASA has also chimed in this year with a really nice article about how to Celebrate Pi Day like a NASA Rocket Scientist

Here is an example of finding out how many times the Mars Rover’s wheels have rotated in its lifetime on the Red Planet:

So how many decimal places must we use for Pi? NASA JPL’s director and chief engineer for NASA's Dawn mission, Marc Rayman, puts this in perspective; Let me summarize his article, How many decimals of Pi do we really need?:

• For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793.
• The spacecraft, Voyager 1 is the furthest space vehicle from Earth right now at approximately 12.5 billion miles away +/- around a million miles. Take a circle with a radius of exactly that size (or 25 billion miles in diameter) and let’s calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, we get a bit more than 78 billion miles. We don't need to be concerned here with exactly what the value is but rather what the error in the value is by not using more digits of pi. So we try cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches, somewhat less than the length of your little finger.

Want to see the square root of 2 to 1 million digits? Click on this link

And remember, “Pi are not square, Pi are round!”

6 comments on “Enjoy a slice of Pi Day”

1. CalcFan
March 15, 2017

Another reference of the number of digits required for Pi is for the trig calculations used in HP calculatiors.  The most sensitive is the tangent function.  Since 1990 HP has used 31 digits for the internal value of Pi (truncated not rounded).

X < > Y,

Richard

2. CalcFan
March 15, 2017

I just found a link related to the posting above.  The article describes pi with lots of examples and even a discussion of measuring it using a 100 foot circle.  It is from an HP Calculator newsletter.  Ooops links not allowed – yet.

Google “HP solve calculator newsletter” and look at October 2011, Issue 25, page 25.

X < > Y,

Richard

3. Steve Taranovich
March 15, 2017

4. Peter.Checkovich_#2
March 16, 2017

Although Pi is universal across all mathematics, is Pi Day celebrated throughout the world?

The only country in the world that uses a M/D/Y format exclusively is the USA. The only other country to use it at all is Canada, which is somewhat schizophrenic due to its French and American-English backgrounds.

The vast majority of countries use some format that orders the time-period-markers in consecutive size-order of the time interval defined. This seems like a natural ordering, but the USA chooses a different ordering.

This leads to an issue that I have never seen a clearly explained. Many of us now communicate via email with others from around the world. Which ordering format should be used? Should the writer use that of the country he/she is a citizen of? Where he/she is currently located? The location of the recipient of the email? If recipients reside in more than one country, then what? For someone who replies to the initial email, should they stay with the initial ordering or switch to their local variant? If several Americans start an email thread using a M/D/Y format, and then someone decides that they want to send a reply and cc someone from Europe, should they go back and edit the previous thread-entries first?

There are similar issues that arise from variants of spelling of English words from around the world, but this is much less likely to create major confusion as a misundersting of dates. Also, using relative terms like yesterday, today or tomorrow can also lead to confusion, depending on the day it is where the sender/receiver are located.

Since the article also discusses the number of decimal places required for various applications, what guidelines are required for the accuracy for converting metric to Imperial measurements? Can one make a round-off fortune by buying tons (or tonnes) of gold in ounces and selling the same gold in kgs? Also, since the ounce is a unit of weight and not mass, can one buy gold in ounces at the equator, and then sell at the North Pole?

Each country so strongly believes that standards are extremely important, it is  imperitive that each country adopts one of its own.

5. Victor Lorenzo
March 18, 2017

Pi Day celebration, I think, is for mathematicians like MAY-4th for Start Wars fans, I don't think it is universal.

In terms of units conversion I find more problematic the fact that several units share the same name, in the same language, and have different magnitudes when compared to other standard magnitudes. The most important point to take into account here is to be sure of the magnitude units we are working with.

How many digits should we use while converting from one unit to other? That depends on the final allowed error for the measurement or the control loop. I find very unconfortable working with mixed imperial/metric defined component footprints as it sometimes makes difficult to define the grid size for PCB routing.

The date/time representation format is another issue as you point. It is a big concern for me when developing Windows applications for runnind in different languages or different locales.It is of more importance when executing queries in databases. You can be working in two instanciations of the system using the same database engine release, and the same application release running on two different windows locales. Of course there are tricks for solving this issue, but you must be always aware that it can show up and create a big mess.

Some countries use the comma as the decimal separator (like Spain) and some others use the dot. And the opposite for the thousands separator. It is very dangerous if not taken properly into account too.

The same hapends when working with CNC machines. Are you generating G-Code in inches or millimeters? It is a common trap for newbies.

The solution? Be careful, very careful, and methodic, and take into account the amount of error allowed when doing conversions, and in programming terms, program defensively, and create a well structured and easy to follow documentation, always.

6. MelBrandle
July 18, 2018

I have always remembered pi being 3.14 my entire life but I know that isn't as accurate as 22/7. During school days, I would be so pissed at the Math problems containing pi because I would always have doubts on whether to use 2 or 3 or even 4 decimal points to increase the level of accuracy for the eventual answer. 1 less decimal point could cause me to end up with a totally different answer which would make me lose a mark. Thankfully that is all over!

This site uses Akismet to reduce spam. Learn how your comment data is processed.