"The difficult is what takes a little time; the impossible is what takes a little longer," said Fridjof Nansen, the 1922 Nobel Peace Prize winner who personally organized the repatriation of more than four hundred thousand prisoners of war after World War I and helped save millions of Russians from starvation.
Wednesday, September 19, 2012
Pascal's Triangle
Do some further research to surprise, awe, entertain and inform us about Pascal's triangle. Stretch your thinking to use mathematical language and to make meaningful connections.
Pascal's triangle is a triangle named after a mathematician named Blaise Pascal. It is a triangle of numbers where the 2 rows of 1's are added as the first number. And continue to add the next number to make the next etc. Pascal is also a physicist, writer, inventor and christian philosopher.
I found out that the row to the power of two equals the sum of all the numbers in that row. For example :row five 5+5+10+10+1+1=thirty two two to the power of five 2x2x2x2x2=thiry two both answers are thirty two.
http://en.wikipedia.org/wiki/Pascal's_triangle : look at the short clip of how pascal's triangle works it really helps you understand the pattern. did you know that in Italy pascal's triangle is reffered to tartaglia's triangle. The diagonals on the left and right edges only contain ones. http://www.bookrags.com/research/pascals-triangle-wom/
Pascal's Triangle is tied to Fibonacci because in Pascal's Triangle the 2 numbers beside each other added together create the next number and in Fibonacci the previous 2 numbers added together create the next number.
Pascal’s triangle is a triangular array in mathematics. It is named after the french mathematician Blaise Pascal. Even though people in Iran, Italy, China, Germany, Greece and India have studied it centuries before him he was the only one to succeed.. Pascal’s triangle was known in China as early as 1261. Blaise discovered the triangle in 1653.
Pascals triangle, and his three dimensial one is called his pyramid or tetrahedron. The triangle is a simple mathematical pattern which adds the two above adjacent digits and puts the answer below. The triangle's starts with one and then continues downward the triangle is completely symetrical in its numbers. If the triangle is left justified and then diagonally connected between the numbers, if the diagonal partners are summed up they become consecutive fibonacci numbers. which may also mean that the triangle could be related to nature.
there is some thing calleed a hockey stick pattern and there is a pattern formed in the hockey stick and the pattern is that the top numbers in the hockey stick adds up and equals the last bottom number
In the second diagonal line it goes 1,2,3, and so on . in the second diagonal line you start by adding 2 and go on adding one to the number you added last time. if you look on google you will find that the lines adda together in some form to make fibonacci numbers.
I found out that it was infact the anicent Chinese who discovered the base idea of the Triangle! Yes,its true,but Blaise Pascal relized its importence and enhanced it.
Blaise lived 39 years,such a short time for a man who developed this triangle!
Also, he created one of the first ever calculaters,a funny little (i mean big) contraption. If you want pictures, go on Wikipedia and search Pascals Calculater
The triangle can be used to look or discover the probability of something, for example: lets say there are five different fruits in a bowl. I want to know haw many combinations of 2 fruits I can create in total. In other words how many combinations of 2 I can get from 5 fruits. The answer is the second place in the fifth row of the triangle which is 10. Keep in mind, the first row is considered to be row #0, and you count the place in the row from the left (also the first number in the row is considered to be 0).
I came across the fact that the third diagonal row in the triangle is formed by triangular numbers: 1, 3, 6, 10, 15, 21, 28 etc. I was wondering what does "TRIANGULAR NUMBER" mean?????
Once you get the hang of it it's so easy! It's just adding!
ReplyDeleteWe found out that the two numbers next to each other add up to make the number below.
ReplyDeleteit goes like add the numbers beside each other then it makes a new number in between(go on
ReplyDeletehttp://www.bing.com/images/search?q=pascals+triangle&view=detail&id=C85187B1CBD2DEA89D884A9C797AD2AF0BB8CB15&qpvt=pascals+triangle&FORM=IDFRIR)
pascal had a religious vision and he quickly jotted down Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the scholars.
ReplyDeletePascal's triangle is a triangle named after a mathematician named Blaise Pascal. It is a triangle of numbers where the 2 rows of 1's are added as the first number. And continue to add the next number to make the next etc. Pascal is also a physicist, writer, inventor and christian philosopher.
ReplyDeleteGemini01 and V.F
I found out that the row to the power of two equals the sum of all the numbers in that row. For example :row five 5+5+10+10+1+1=thirty two
ReplyDeletetwo to the power of five 2x2x2x2x2=thiry two both answers are thirty two.
http://en.wikipedia.org/wiki/Pascal's_triangle : look at the short clip of how pascal's triangle works it really helps you understand the pattern.
ReplyDeletedid you know that in Italy pascal's triangle is reffered to tartaglia's triangle. The diagonals on the left and right edges only contain ones. http://www.bookrags.com/research/pascals-triangle-wom/
wow thats interesting
ReplyDeletePascal's Triangle is tied to Fibonacci because in Pascal's Triangle the 2 numbers beside each other added together create the next number and in Fibonacci the previous 2 numbers added together create the next number.
ReplyDeletePascal’s triangle is a triangular array in mathematics. It is named after the french mathematician Blaise Pascal. Even though people in Iran, Italy, China, Germany, Greece and India have studied it centuries before him he was the only one to succeed.. Pascal’s triangle was known in China as early as 1261. Blaise discovered the triangle in 1653.
ReplyDeleteand also if you do a zigzag they x2 each pair
ReplyDeletethe odd numbers in pascal's triangle seem to make mini triangles
ReplyDeletePascals triangle, and his three dimensial one is called his pyramid or tetrahedron. The triangle is a simple mathematical pattern which adds the two above adjacent digits and puts the answer below. The triangle's starts with one and then continues downward the triangle is completely symetrical in its numbers. If the triangle is left justified and then diagonally connected between the numbers, if the diagonal partners are summed up they become consecutive fibonacci numbers. which may also mean that the triangle could be related to nature.
ReplyDeletethere is some thing calleed a hockey stick pattern and there is a pattern formed in the hockey stick and the pattern is that the top numbers in the hockey stick adds up and equals the last bottom number
ReplyDeleteIn the diagonal starting at 1 there is a pattern that adds 2 then 3 then 4 and so on.
ReplyDeleteit was thought up around the same time in persia & China as well as the diagonal lines add up to fibbonachi
ReplyDeletes.l
In the second diagonal line it goes 1,2,3, and so on .
ReplyDeletein the second diagonal line you start by adding 2 and go on adding one to the number you added last time. if you look on google you will find that the lines adda together in some form to make fibonacci numbers.
I found out that it was infact the anicent Chinese who discovered the base idea of the Triangle! Yes,its true,but Blaise Pascal relized its importence and enhanced it.
ReplyDeleteBlaise lived 39 years,such a short time for a man who developed this triangle!
Also, he created one of the first ever calculaters,a funny little (i mean big) contraption. If you want pictures, go on Wikipedia and search Pascals Calculater
It's really easy once you find out that it's just adding. lolz
ReplyDeletewhy was the pascals triangle made
ReplyDeletewow that's interesting!
ReplyDeleteThe triangle can be used to look or discover the probability of something, for example: lets say there are five different fruits in a bowl. I want to know haw many combinations of 2 fruits I can create in total. In other words how many combinations of 2 I can get from 5 fruits. The answer is the second place in the fifth row of the triangle which is 10. Keep in mind, the first row is considered to be row #0, and you count the place in the row from the left (also the first number in the row is considered to be 0).
ReplyDeleteI came across the fact that the third diagonal row in the triangle is formed by triangular numbers: 1, 3, 6, 10, 15, 21, 28 etc. I was wondering what does "TRIANGULAR NUMBER" mean?????
ReplyDeleteCheck out these videos and you will get an idea of triangular numbers:
ReplyDeletehttp://www.youtube.com/watch?v=TgQn8snKGtw
http://www.youtube.com/watch?v=ERdhPGslNw8&feature=related