Author Alex Bellos has been rightly praised for his fascinating book Alex's Adventures in Numberland. It is a book full of mathematical gems presented in an accessible style not normally associated with mathematics books - which possibly explains it's success. One of the chapters is devoted to the study of pi and the people who have pushed back the boundaries of this number - a dry topic transformed into a engrossing read.
For those who need a reminder - pi is the ratio of a circle’s circumference to its diameter. As Bellos puts it ”...if you take the diameter of a circle and curve it around the circumference, you will find that it fits just over three times.” It is that “just over” bit that makes pi interesting. The “just over” bit is actually an irrational fraction - meaning it never ends - it simply goes on forever. The accuracy of pi has been calculated to a ridiculous degree - billions of digits. According to Bellos, manufacturers of precision instruments only need an accuracy of four decimal places so the quest for a more and more accurate figure for pi is no longer driven by any practical reasons. However, early methods of calculation were ingenious and the chapter in Bellos’ book provides an entertaining overview of many of them.
The chapter contains this discussion of pi in, of all places, the Bible.
"...A line in the Bible reveals a situation in which pi is taken a 3: 'Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about' (I Kings 7:23)".
Thus the Bible is on shaky ground from a mathematical perspective. After a very brief discussion on some squeamish “explanations” from devote believers on what the bible may have meant when giving that description Bellos throws in an absolute gem.
"A mystical explanation is much more enticing: due to the peculiarities of Hebrew pronunciation and spelling, the word 'line', or qwh, is pronounced qw. Totting up the numerological values of the letters gives 111 for qwh and 106 for qw. Multiplying three by 111/106 gives 3.1415, which is pi correct to five significant figures.”
Today we would call this numerology - but the practice has a long history. Traditionally the practice of ascribing numerical values to words was known as gematria and was wide-spread amongst the ancient Greeks.
I’m not sure what I find hardest to believe - that someone in Biblical times not only knew pi to five significant figures and could hide it via gematria in a passage to be decoded by the enlightened...or that purely random chance and an accident of linguistics has delivered pi to five significant figures - in a passage describing a circle.
What has this mathematical musing have to do with education? Two things. As teachers we don’t always have the answers - and we should admit this to our students - not necessarily in relation to the concepts discussed here but in general terms. The second is that the simple fascination of the unknown and the delight of exploration that is associated with mathematics should be shared with our students. Again, not necessarily these concepts, but with mathematics in general. We should present mathematics as a subject full of fascination to be explored rather than allow it to be reduced to a collection of rote exercises, algorithms and meaningless formulae.
The worth of a word:
Gematria is an ancient belief. For most of us it is as valid as the notion of a flat earth or that the earth was a disk sitting on the back of a turtle floating through space. However, if you want to calculate the numeric value of certain words or names then clicking here will take you to a site that may be useful as well as amusing. The site also provides words with the same numerical value as the text you input.
Have fun.
Credits:
Pi graphic: https://www.msu.edu/~greenke5/webquest/Graphics/pi%20pic.JPG
For those who need a reminder - pi is the ratio of a circle’s circumference to its diameter. As Bellos puts it ”...if you take the diameter of a circle and curve it around the circumference, you will find that it fits just over three times.” It is that “just over” bit that makes pi interesting. The “just over” bit is actually an irrational fraction - meaning it never ends - it simply goes on forever. The accuracy of pi has been calculated to a ridiculous degree - billions of digits. According to Bellos, manufacturers of precision instruments only need an accuracy of four decimal places so the quest for a more and more accurate figure for pi is no longer driven by any practical reasons. However, early methods of calculation were ingenious and the chapter in Bellos’ book provides an entertaining overview of many of them.
The chapter contains this discussion of pi in, of all places, the Bible.
"...A line in the Bible reveals a situation in which pi is taken a 3: 'Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about' (I Kings 7:23)".
Thus the Bible is on shaky ground from a mathematical perspective. After a very brief discussion on some squeamish “explanations” from devote believers on what the bible may have meant when giving that description Bellos throws in an absolute gem.
"A mystical explanation is much more enticing: due to the peculiarities of Hebrew pronunciation and spelling, the word 'line', or qwh, is pronounced qw. Totting up the numerological values of the letters gives 111 for qwh and 106 for qw. Multiplying three by 111/106 gives 3.1415, which is pi correct to five significant figures.”
Today we would call this numerology - but the practice has a long history. Traditionally the practice of ascribing numerical values to words was known as gematria and was wide-spread amongst the ancient Greeks.
I’m not sure what I find hardest to believe - that someone in Biblical times not only knew pi to five significant figures and could hide it via gematria in a passage to be decoded by the enlightened...or that purely random chance and an accident of linguistics has delivered pi to five significant figures - in a passage describing a circle.
What has this mathematical musing have to do with education? Two things. As teachers we don’t always have the answers - and we should admit this to our students - not necessarily in relation to the concepts discussed here but in general terms. The second is that the simple fascination of the unknown and the delight of exploration that is associated with mathematics should be shared with our students. Again, not necessarily these concepts, but with mathematics in general. We should present mathematics as a subject full of fascination to be explored rather than allow it to be reduced to a collection of rote exercises, algorithms and meaningless formulae.
The worth of a word:
Gematria is an ancient belief. For most of us it is as valid as the notion of a flat earth or that the earth was a disk sitting on the back of a turtle floating through space. However, if you want to calculate the numeric value of certain words or names then clicking here will take you to a site that may be useful as well as amusing. The site also provides words with the same numerical value as the text you input.
Have fun.
Credits:
Pi graphic: https://www.msu.edu/~greenke5/webquest/Graphics/pi%20pic.JPG
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