Algebra 1 - Thompson - Y band

Binary Sequences

bstroman — Sat, 20 Dec 2008 07:41:45 -0500

Well, for my project, Me and other fellow classmates: Alaya White, Marina Stuart, and Tariq Smith were focusing on the binary sequence.

In 1679, Gottfried Wilhelm von Leibniz was the first person to ever discover binary numbers. What are binary numbers? Let's just say that the only number that are used 1 and 0. In this matter, they represent letters and numbers.

The Numbers from 1-20

0 =     0
1 =     1
2 =    10
3 =    11
4 =   100
5 =   101
6 =   110
7 =   111
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111
16 = 10000
17 = 10001
18 = 10010
19 = 10011
20 = 10100

Capital Letters

A=01000001
B=01000010
C=01000011
D=01000100
E=01000101
F=01000110
G=01000111
H=01001000
I=01001001
J=01001010
K=01001011
L=01001100
M=01001101
N=01001110
O=01001111
P=01010000
Q=01010001
R=01010010
S=01010011
T=01010100
U=01010101
V=01010110
W=01010111
X=01011000
Y=01011001
Z=01011010

Lower Case Letters

a=01100001

b=01100010
c=01100011
d=01100100
e=01100101
f=01100110
g=01100111
h=01101000
i=01101001
j=01101010
k=01101011
l=01101100
m=01101101
n=01101110
o=01101111
p=01110000
q=01110001
r=01110010
s=01110011
t=01110100
u=01110101
v=01110110
w=01110111
x=01111000
y=01111001
z=01111010

That is binary codes for letters and numbers. Some people always ask if the binary sequence similar to the binary code. In my personal opinion, just because they use the same two numbers, doesnt mean that they are exactly the same thing. See the numbers and letters above this, is the binary code which is usually used on computers. As far as the binary sequence:

I dont think people would want to follow that sequence.

In conclusion, I think a the binary code is easier than the binary sequence, even though the binary code has alot of numbers that people wouldn't stand.

Algebra 1 - Thompson - Y band

Power Sequences by Maxine Hayman

mhayman — Thu, 04 Dec 2008 11:50:03 -0500

In this post to drupal I will be explaining what me and my fellow classmates had to do for Mr. Thompsons Math class.

Everyone in our math class was broken up into groups of 4 or 5 students. All of groups got different assignments such as The Fibonacci Pattern, Sierpinski Triangle, Binary sequence, Triangular and Rectangular Sequences, and Power sequences.

The group I was in was power sequences and with power sequences there are many types of power sequences. What we had to do was study our sequence and find out what it was, what was it used for, interesting information and who uses it and why.

I found out that a power sequence is a sequence of numbers or artifacts that use the power method. For example if I was using the power of one my sequence would go as follows 3, 9, 18, 324… this is what I mean bye a power sequence.

In my math team we were in a groups of 5. The people in my group were Lamaya Mapp, Joseph Parisi, Anna Roman, and William Marsh. All of my references I received from my classmate’s blog and my algebra 1 teacher Ms. Thompson.

Algebra 1 - Thompson - Y band

The Fibonacci Pattern By Nia Berry

nberry — Thu, 13 Nov 2008 17:49:52 -0500

Nia Berry November10, 2008

Orange Stream-Y band

The FibonacciPattern

In math class with Ms. Thompson we were assigned different math patterns. My group which consists of myself,Francessca, Blase, and Sammantha were given the Fibonacci Pattern. Leonardo ofPisa created the Fibonacci pattern in 1202. The sequence follows a patternwhere the next term is the sum of the 2 previous terms. The formula for thispattern is tn=t(n-1)+t(n-2). The Fibonacci pattern will look like this: 0 1 1 23 5 8 13 21 …….. When trying to use this pattern all you really need to do isadd.

http://teacherweb.com/fl/meadowlawnms/michaeltaylor/ft051011.gif

Algebra 1 - Thompson - Y band

Jasmine Gladden, Sierpinski Triangle

jgladden — Thu, 13 Nov 2008 12:39:54 -0500

Jasmine Gladden
Blue
10-9-08
Sierpinski Triangle
My group had the Sierpinski Triangle. The people that I worked with to get the following information are Kyla, William, and Jason. The correct way to pronounce it is (SIeR-PINn-SkI). The person who discovered this fascinating triangle was named Waclaw Sierpinski. A Sierpinski Triangle is a geometric pattern formed by connecting midpionts of the sides of the first triangle. In your imagination you will think your creating triangles infinitely as many times. The type of math that this triangle takes place in is geometry, at the same time this is an arithmetic sequence, that goes with an equation to make it algebra. The formula for this Sierpinski Triangle would be (n) equals 3^(n-1). The start of the sequence, if it is a red triangle, is term n0 = 1triangle. Every term you remove a triangle peace from every center of the newly created triangle. This process theoretically could go on forever. It makes life/math easier because it shows how at a certain point successive stages can no longer be told apart from each other. However, here is a picture of the Sierpinski Triangle.

Algebra 1 - Thompson - Y band

Fibonacci Sequence, Francesca Brennan

fbrennan — Thu, 13 Nov 2008 11:33:15 -0500

Group Members: Blase, Nia, Samantha, and Francesca

Leonardo of Pisa invented the Fibonacci Sequence in 1202. It was used in many methods of biology. The Fibonacci Sequence has a purpose, which is to organize and investigate a numerical pattern. Also, it helps to search for and identify evidence of mathematical patterns in nature.

The Fibonacci Sequence is arithmetic, and it uses addition to find the next term of numbers. In this particular sequence each of the consequent numbers are equal to the previous two numbers, which means that to find the next term you must take the first two numbers before it and add them together. In this sequence that is the constant occurring pattern. This sequence is known as a recurrence relation.

In this particular sequence there is a formula to find the nth term, F( n ) = (a^n - b^n)/(a - b). An example of the Fibonacci Sequence is, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...,, because when looking at this you can clearly see that to find each term the two numbers before it must be added together. This sequence is helpful in many ways, because it can in fact use mathematical programming to find the period containing the purpose of one variable. Also, as I stated before this factor makes it a great sequence to use when determining pairs or anything in biology.

Algebra 1 - Thompson - Y band

Sierpinski Triangle

kcarden — Thu, 13 Nov 2008 10:58:28 -0500

I am Kyla Carden and I am doing this project for my Algebra 1 class. My whole class split up into groups and researched different sequence. My group was made up of Jasmine, Will F., Jason, and myself. Our group was assigned the Sierpinski Triangle. Waclaw Sierpinski founded the Sierpinski Triangle. The Sierpinski Triangle is a geometric pattern that is formed by connecting the middle points of the sides of the triangle. When you do this you create 4 triangles. You subtract the middle triangle at the bottom from the sequence and so on, and so on. This sequence contains an infinite amount of triangles. Although this applies to geometry it has an arithmetic formula, which is (n) = 3^(n-1).

Algebra 1 - Thompson - Y band

All about Binary sequence

awhite — Wed, 12 Nov 2008 21:09:05 -0500

Our mini project was to research our assigned sequence and teach someone something new. My assigned sequence was Binary sequence and my group members were Marina Stuart, Briana Stroman, and Tariq Smith. Here is more information about Binary sequence.
Gottfried Wilhelm von Leibniz first formally described the binary number system and its operations in writing in 1679. He is also the same person who co-discovered calculus. Binary Sequence is a sequence that has the numbers 0 and 1 representing numbers and letters. Some people believe that Binary sequence is an easier strategy in order to represent numbers and the letters of the alphabet. I believe the total opposite. I think that it is too much to remember the formula for Binary sequence and it may be too confusing for some people. The formula for Binary sequence is below:
The formula for numbers:
0 =     0
1 =     1
2 =    10
3 =    11
4 =   100
5 =   101
6 =   110
7 =   111
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111
16 = 10000
17 = 10001
18 = 10010
19 = 10011
20 = 10100

The formula for capital letters:

The formula for lower case letters:

a=01100001

Algebra 1 - Thompson - Y band

Binary Sequences by Marina Stuart

mstuart — Wed, 12 Nov 2008 20:26:30 -0500

Our assignment in algebra 1 was to research a different sequence with a group of three or four people and report to each other on information we get. I was assigned binary sequences. I worked with Alaya White, Brianna Stroman, and Tariq Smith. I have now learned a lot about binary sequences and why they are.

This is how binary sequences can express any number.

(http://math.editme.com/Binary)

Binary sequences are used in the circuits of calculators and computers to represent numbers. This is very helpful because with out them computers and calculators could not function very well. Binary Sequences relate to binary codes in the way that they both use 1 and 0s and are used in computers. Binary sequence can also be useful in adding up different sums.
Binary sequences are very important in our daily lives, when dealing with computers, and in math class, it is a very essential sequence to understand and know.

Example Questions:

1)
1 2 4 8 16
Write the following numbers in binary numerals
5
14
19

2)
Translate the following number
1 2 4 8 16
0 1 0 1 1

Algebra 1 - Thompson - Y band

Triangular and Rectangular Sequences

blewis — Wed, 12 Nov 2008 18:12:01 -0500

In a Triangular sequence it follows a rule/formula of n(n+1)/2.It is used for probability problems,but it can be used for puzzles as well and also in Algebra .It's name is Pascal's Triangle looking like a triangle with many numbers within it.It's purpose in the field of Algebra is, Pascal's Triangle is used for raising the power of a polynomial x+1. In probability, it can be used to find combinations and in puzzles it serves as a good thinking tool for the mind.The way that Pascal's Triangle is solved and also the way the pattern is learned by taking the two numbers above a blank square and adding them together. Also, the sum of a row is the above row multiplied by two. The first row one square has a sum of 1.In a Rectangular Sequence it follows a rule/formula of n*(n+1).It has many uses such as again puzzles and again like the triangular sequence it is used in probability as well.It looks like a rectangle but within it there are many numbers

Algebra 1 - Thompson - Y band

Triangular and Rectangular Sequences by Dylan Lonergan

Dylan Lonergan — Wed, 12 Nov 2008 16:58:24 -0500

Recently, our algebra class was required to research different sequences as part of several "mini-projects." Students were divided into groups, and each was assigned a different sequence to research, and in the end posting our discoveries on Drupal. The group I was in was assigned triangular and rectangular sequences. I was then appointed to the research of triangular sequences, so naturally I specialize in them.

Triangular sequences are sequences that use triangular numbers (such as 1, 3, 6, 10, 15, 21, etc.). The sequence is actually quite famous, and is commonly known as Pascal's Triangle, named after the French mathematician and scientist, Blaise Pascal. It was not actually created by him (the truth is it was known in China circa 1300 A.D.), but it may have been named after him because of his research and work in the subject of probability. Which brings me to my next point- what is it used for? Pascal's Triangle is used in probability as well as algebra. In algebra, Pascal's Triangle is used for raising the power of a polynomial x+1. In probability, it can be used to find combinations. So, it provides a much simpler way to solve those problems in algebra and probability.

Pascal's Triangle is solved by taking the two numbers above a blank space in the famous Triangle, and then adding them. Also, the sum of a row is the above row multiplied by two. The first row (one space) has a sum of 1. The formula for the Triangle is n(n+1)/2. Thus, Pascal's Triangle uses multiplication, addition, and division. Because of the method of solving it, Pascal's Triangle is also sometimes used as a puzzle (I, for one, was given Pascal's Triangle as a puzzle by my science teacher in 8th grade last year). This concludes my analysis of Pascal's Triangle and the triangular number sequence. Personally, I find it very interesting. The triangular number sequence is not limited only to Pascal's Triangle, however- it is also a part of the Fibonacci Sequence, which, coincidently, was researched by another group in this project, so I won't get into detail about it.

Algebra 1 - Thompson - Y band

Fibonacci Sequences Presented By Samantha Beattie

sbeattie — Mon, 10 Nov 2008 22:18:43 -0500

The Fibonacci sequence is an arithmetic sequence. It uses addition to find the next term number. The way a Fibonacci sequence works is that t1 will always be zero and t2 will always be one. It normally looks like: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765 . . .
The formula that is always used to find the nth term in this type of sequence is F (n) = (a^n - b^n)/(a - b). This sequence initially came from Leonardo of Pisa and introduced in the year 1202. It was first used in biology. It helped to find different numbers of species and the amount of pairs in each month. A question once answered through this, by this same man was: How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?
What is the purpose of this sequence you ask? The purpose is to organize and investigate a numerical pattern. Fibonacci sequences are actually more that meets the eye. There is more to them than you would really expect. The importance tells it all!
The importance of a sequence like this would be:
1. Is used in mathematical programming to find the interval containing the minimizer of a function of one variable.
2. Occurs in nature, art, music, and math
3.Just about everything has to do with Fibonacci numbers. Plants have a number of leaves, which would be a Fibonacci number. This can also be for the number of petals on a flower or seeds in a flower head.
Example: the number of spirals that curve to the left and the number that may curve to the right would come out to be adjacent numbers in a Fibonacci sequence.
4. It is important in art and music due to the ratio between successive Fibonacci numbers approximates an important constant called "the golden mean" or sometimes phi, which is approximately 1.61803.
That’s all.

Algebra 1 - Thompson - Y band

Power sequences by William Marsh

wmarsh — Mon, 10 Nov 2008 12:41:26 -0500

In this drupal post, I will be explaining power sequences. I'm sure that the first and foremost question that comes to mind for many is "what is a power sequence?"; a power sequence is a pattern or sequence of numbers that follows an exponential rule. For example if the first term of a power sequence were three and the rule of it was to follow the second power the first several terms would be as follows: 3, 9, 81… There are technically two ways of saying something is a power sequence. The first would obviously be a power sequence however the second would be known as an exponential sequence; or a sequence that uses exponents. Power sequences are not used often because they are used solely when something rises or falls exponentially; which is not very common. It can make our lives earlier because if something is being affected to such a degree that it is exponential growth or decline; knowing the pattern would allow us a brief 'glimpse into the future' to see what was going to happen and give us more time to prepare or reverse the actions if necessary. It is important to understand how power sequences work because otherwise there is no way of predicting exponential patterns accurately. While I was studying this, I worked in a group of my classmates. Their names are Lamaya Mapp, Joseph Parisi, Anna Roman and Maxine Hayman.

I wish I could list my citations but unfortunately I received all of my resources directly from my math teacher, Ms. Thompson.