alone. Zoom out, we discover this pattern known as the Sierpinski Triangle. Same goes for the pyramid.
We also have the Fibonacci sequence which is a bit hard to spot.
You have possibly worked with probabilities with this sequence in school. A famous example is flipping coins. You will either get heads or tails. Suppose you throw it times. The possible number of results can be found in row in Pascal’s triangle. The total possibilities of either heads or tails appearing times, ( ≤ ) , is shown in the array with the ℎ representing the total possibilities. Let’s draw a table:
Throws
Possible Results
Pascal’s Triangle
Throws
Possible Results
Pascal’s Pyramid
H T S
1 1 1 1 2 1 2 1 2
H T
1 1 1 2 1 1 3 3 1
1
1
HH HT TH TT
HH HT TH TT TS ST SS SH HS
2
2
HHH HHT HTH THH HTT THT TTH TTT
3
…
…
…
…
…
…
The same theory applies to the pyramid model. Suppose a very skilled coin flipper has 1 3 the probability of landing a coin standing straight up, the table would look like the one above on the right. So where does this perfect creation come from? We need to look back to France in 1654. In 1654 Blaise Pascal completed his Traité du Triangle Arithmétique and later the titular array was given the name Pascal’s Triangle. However, the original discovery of this array, which later led to the more famous Pascal’s Triangle, actually took place in China. In the 13 th century, mathematician Yang Hui officially presented the triangle. Hence it is still called the Yang Hui Triangle, 杨辉 三角 , in China. The earliest official mathematics in China dates back to the Shang Dynasty (1600-1050 BC). Back then, calculations were done using rods of bamboo. This first number system could even handle complex calculations pretty well. It was, however, just a counting method- the written numbers were not that efficient. Jumping 1500 years ahead, the numeric system had improved a lot to make mathematics more accessible. In the 13 th century, China’s mathematics reached its peak as many new features were discovered by mathematicians and the government decided to make education of mathematics to everyone possible.
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