# The 18 equations that changed the course of history.

**1. The Pythagorean Theorem**

**2. Logarithms**

**3. Calculus**

**4. Law of Gravity**

**5. The square root of -1**

**6. Euler's Polyhedra Formula**

**7. Normal distribution**

**8. Wave Equation**

**9. Fourier Transform**

**10. Navier-Stokes Equations**

**11. Maxwell's Equations**

**12. Second Law of Thermodynamics**

**13. Relativity**

**14. Schrodinger's Equation**

**15. Information Theory (''ccFound belongs here'')**

**16. Chaos Theory**

**17. Black-Scholes Equation**

**18.**The Bitcoin Supply Formula – Explained

**i=0** – This is the lower **limit** of the equation. It represents the inital the initial epoch of time. When the bitcoin protocol was first discovered, we were in the first epoch, when i=0. For each halving epoch, i is incremented +1.

## 32 – 32 is the upper limit for the equation. 32 indicates the total number of halving epochs that will occur within the Bitcoin protocol. For each halving period, i is incremented from 0 (the lower limit) through to and including 32 (the upper limit)

## 210,000 – 210,000 is a function of the supply issuance of new bitcoin, which coincides with the number of blocks each halving. Each period of 210,000 blocks is referred to as one epoch. After each epoch of 210,000 blocks, the summation equation limit (i) is increased +1. The Bitcoin protocol is specifically designed to control the rate of release of new blocks to an average of one block every 10mins. It therefore takes around ~4years (210,000 x 10mins) for each epoch of 210,000 blocks.

## 50 – The initial block reward during the first epoch of Bitcoin’s history was 50. However, as we will see soon, this number is halved during each epoch.

## 2 – This number is how we obtain the term “halving”. At the end of each epoch, the block reward is divided by 2, in other words… it halves.

## “i” = As mentioned above, throughout the summation equation, i is incremented to within the limits of the summation equations and to coincide with the current epoch. During the first epoch, i was 0 and the equation is performed. During the second epoch, i is 1 and the equation is performed again. When we substitute i into the equation, it acts as the exponent of the number 2. Whoa!! Enough math terms already. An exponent is another term for power. Example: When i = 3, within the equation we now see 23, which basically means 2 to the power of 3, otherwise 2 x 2 x 2. Similarly, if i were equal to 4, it becomes 2 to the power of 4 (24). Which is another way of saying 2 multipled by itself 4 times, e.g 2 x 2 x 2 x 2. The exponent, therefore directly affects the halving intital block reward by (which was initially 50) each epoch by acting as the exponent on the number 2.

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