Blaise Pascal
Pascal is probably most famous for his
contributions to physics but he also had many contributions
to mathematics. At a very young age he mastered Euclid's
Elements which is a series of books describing complex
mathematical theorems and proofs. Blaise would later use his
understandings of these concepts in order to produce and
find his own proofs and theorems.
Pascal's Theorem
Pascal's first theorem that he found was
one he found when studying Desargues' work on conic
sections, it is now known as Pascal's Theorem. The theorem
states that given a hexagon inscribed inside a conical
section, the three parts of the continuations of each
opposite side meet along a straight line known as the Pascal
Line.
 |
| Example of Pascal's Theorem Picture from: Mathworld |
Pascal's Triangle/Probability Theory
Pascal's Triangle or the arithmetic
triangle is a triangle with ones at the top and along the
right and left sides where the next number is found by
adding together the two above it(see left). This pattern had
been studied long before Pascal but he published the Traite
du Triangle Arithmetique which brought
together many of the results and patterns that had been
found in the triangle and used them for various problem
solving and probability scenarios.
Some of the patterns found within the
triangle include:
-counting numbers in a row
-Triangular numbers in a row(ex. Number of blocks to stack a
triangle, 1, 3, 6, 10, etc.)
-Even numbers reveal a sierpenski Triangle
pattern(neverending repeating triangle pattern)
-Finding various probability outcomes
Figure from: Wikipedia