Pascal's triangle is a mathematical concept originally developed by the Chinese that was later popularized by French mathematician Blaise Pascal. It arranges numbers in triangular form according to binomial coefficients and can be used for applications in algebra, probability, and counting patterns like Catalan numbers. Pascal discovered the importance of the triangle in 1653 and it is constructed by adding numbers above following the rule of their sum being the numbers directly next to them.
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Pascals Triangle
1.
2. Pascal’s triangle was originally developed by the
Chinese
Blaise Pascal was the first to actually realize the
importance of it and it was named after him
Pascal's triangle is a math triangle that can be
used for many things.
Pascal's Triangle is used in algebra and
probability
Pascal's triangle is the way to use an amount out
of numbers in a divisible way
To solve Pascal's ways you have too add the two
numbers that are next to each other shown in the
diagram on next slide.
3.
4. Hockey Stick Pattern- The hockey stick
pattern is when you can start at any number 1
that borders Pascal’s triangle and make a
diagonal of any size to the right or left. Then
go one additional hexagon to the opposite of
your diagonal. The sum of the diagonal
should equal the ending hexagon.
Prime Numbers-When the first number of the
hockey stick is 1 then the second number will
be divisible of the rest of the hockey stick.
The 1 is a Prime number but, this makes the
rest of the numbers divisible by each other.
5.
6. Born June 19, 1623 and died on August 19,
1662 at the age of 39.
He was a French mathematician, Physicist, and
religious philosopher.
Discovered the importance of the Pascal’s
triangle. It happened in 1653
Invented one of the first mechanical
calculators.
He was educated by his father.
In 1659 he came down with an illness that cost
his life.
We use the pascal’s triangle in math such as
Geometry.
7.
8. The Catalan numbers express the number of
ways that a polygon with N sides can be
divided into triangles.
Diagonals that are drawn are not allowed to
intersect.
The rule for Catalan Numbers is--------
Some Catalan Numbers include
1, 2, 5, 14, 42, 132…
Catalan Numbers can be found in Pascal’s
triangle.
Pascal’s Triangle and Catalan Numbers are
related to each other.
9.
10. Pascal’s Triangle-The way to use an amount
out of numbers in a divisible way.
Catalan Numbers-How polygons can be
divided into a number of triangles.
Geometry-The study of shapes and angles.
Probability-The number used too describe
the chance of an event occurring.
11. Complete this Pascal’s
triangle and find all
of the Catalan
numbers.
Remember, Pascal’s
triangle starts off
with a one. Try to find
out some hockey
stick pattern.
