## Numbers in the “Fundamentalis Tabula Arithmetica”

Does anyone know anything about the "Fundamentalis Tabula Arithmetica" or what could be special about the numbers 106 and 117 that would make Europeans in the 1600s want to know their multiples? Googling reveals nothing about a "Fundamentalis Tabula Arithmetica". Is the word "Fundamentalis" really Latin?

From: Alex Bellos

Date: Mon, Jul 11, 2011 at 11:01 AM

Subject: [math-fun] tables

To: math-fun

Hi - I've just received an email from a reader who saw in a Cologne museum a document called Fundamentalis Tabula Arithmetica from 1638. It is a table of multiples for all the numbers up to 100 and also the tables for these five numbers:

106, 117, 256, 318 and 365

It's pretty obvious why 256 and 365 are included.

Might anyone have any thoughts as to why 106, 117 and 318 (3x106) are also included?

Alex

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117 days is pretty close to the synodic period of Mercury en.wikipedia.org/wiki/Orbital_period -- the period with which the relative positions of Mercury and the sun, as seen from Earth, repeats. No idea on 106. – David Speyer Jul 15 2011 at 3:53
Perhaps these numbers have some meaning in the liturgical calendar (possibly for calculating the date of Easter?). However, some quick browsing on Wikipedia didn't produce any good leads. – Henry Cohn Jul 15 2011 at 4:08
I'm going to guess 318m as the diameter of a circle of circumference 1km. – Gjergji Zaimi Jul 15 2011 at 4:14
That's funny: I had an almost equivalent thought, but it's much closer to 999m. One of the more creative rationalizations for the Biblical passage that seems to assert $\pi = 3$ is that the word for "circumference" is spelled with a normally superfluous silent letter (קוה instead of קו) that increases its numerical value by a factor 111/106 that's quite close to $\pi/3$ (remember $355 \cong 113\pi$ and $22 \cong 7\pi$; subtract to get $333 \cong 106 \pi$). That said, it's rather far-fetched... – Noam D. Elkies Jul 15 2011 at 5:04
According to the historians, the Middle ages lasted until the 15th century, not the 17th. – Hans Stricker Jul 15 2011 at 17:17

Regarding 318, Vincent Forest Hopper writes on p.75 of "Medieval Number Symbolism" (Dover):

"...various of the Church Fathers began to write figurative interpretations of the biblical texts. They found precedent for giving importance to numbers in the precise directions given for the dimensions of the tabernacle, and in the testimony of the Book of Wisdom that 'God has arranged all things in number and measure.' Early interpretation of scriptural numbers is concerned only with the most prominent of them, such as the 12 springs and 70 palm trees of Elim, and the 318 servants of Abraham..." Something of the attitude of gnosis; that is, of scriptural mysteries hidden from the layman, is to be seen in an interpretation of Barnabas: 'Learn then, my children, concerning all things richly, that Abraham, the first who enjoined circumcision, looking forward in spirit to Jesus, practised that rite having received the mysteries of the three letters. For [the Scripture] saith, 'And Abraham circumcised 10, and 8, and 300 men of his household.' What, then, was the knowledge given to him in this? Learn the 18 first and then the 300. The 10 and 8 are thus denoted. Ten by I and eight by H. You have [the initials of the name of] Jesus. And because the cross was to express the grace [of our redemption] by the letter T, he says also 300. No one else has been admitted by me to a more excellent piece of knowledge than this, but I know that ye are worthy.'"