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In certain verses of the Bible, approximations for the mathematical constants $\pi$ and $e$ (Euler's number) can be found using gematria. Those approximations are accurate up to 5 significant figures. However, the approximations are off by a power of 10 and the formula used is quite complex.

Mathematical background
The constant π can be defined as the ratio between the circumference and the diameter of a circle. Being an irrational number, π has an infinite decimal expansion which contains no apparent pattern. Throughout the centuries, humanity has tried to approximate π as accurate as possible. Before Archimedes (250 BC), the best approximation for π was $$\frac{22}{7}=3.14285...$$ which is accurate up to 3 significant figures. The actual decimal expansion of π starts with 3.14159...

The constant $e$ (Euler's number) can be defined as the limit of $$(1+1/n)^n$$ as $$n$$ approaches infinity. Contrary to π which is known from antiquity, Euler's number was first discovered by Jacob Bernoulli in 1683. Euler's number is the base of the natural logarithm. It's decimal expansion starts with 2.71828....

Together with the imaginary unit i, π and $e$ lie at the basis of mathematics.

The Bible verses
The first relevant Bible verse is Genesis 1:1. It is the first verse of the Book of Genesis, which is in turn the first book of the Bible. In English, the verse reads as follows:"In the beginning God created the heaven and the earth. (Genesis 1:1)" The Book of Genesis was originally written in Hebrew. Being part of the Torah, it was written before 250 BC.

The other relevant verse is John 1:1. This is the starting verse of the Gospel of John, which is one of the four gospels at the start of the New Testament of the Bible. The verse reads as follows:"In the beginning was the Word, and the Word was with God, and the Word was God. (John 1:1)"The Gospel of John was written in Greek. It was written before 110 AD.

Both verses contain the phrase "in the beginning". This phrase is also the Hebrew name of the Book of Genesis.

Gematria
In gematria, letters and words are given numerical values using an alphanumerical cipher. The value of a word is calculated by adding the values of the individual letters of the word. In order to obtain the approximations for π and $e$, the following formula has to be used:

$$\frac{\text{number of letters} \cdot \text{product of values of all letters}}{\text{number of words}\cdot\text{product of values of all words}}$$

For example, for Genesis 1:1 the number of letters is 28. To calculate the product of the values of all letters, the 28 corresponding numbers have to be multiplied with each other.

As a result, the formula gives for Genesis 1:1:

$$3.14155...\cdot 10^{17}$$

and for John 1:1:

$$2.71831...\cdot 10^{40}$$

When we omit the powers of 10 and round to 5 significant figures, we obtain 3.1416 and 2.7183 respectively. Those are exactly the values of π and $e$, rounded to 5 significant figures.

Discussion
According to some the phenomenon might be a coincidence, but others think that it is a sign from God.