WPP # 10 Unit L Concepts 9-14

Create your own Playlist on MentorMob!

WPP #9 Unit L Concepts 4-8

Create your own Playlist on MentorMob!

Fibonacci Beauty Ratio Reflective Essay (Extra Credit)

415

Golden ratio in human body

In the first video they introduce a man by the name of fibonacci and his numbers. His numbers are divided and numbers close in proximity are produced. The golden ratio is a number, 1.6180339887. Artist , scientists, and sculptors use this number ratio to build their mater pieces. The number was used by many famous painters to make their work "beautiful".

 

Fibonacci and the golden mean

In 1201 Fibonacci studied mathematics but first introduced Christian religion to the world. He wanted to observe the number of bunny rabbits that were born each year. In conducting this expedient he found that the numbers held a significant pattern. Each number in the series was equivalent to the two previous numbers sum in the sequence. This was the beginning of the unlocking of many other things. It helped in the field of botany. It also helped with the architecture of buildings.

 

Nature by numbers

In this video no words are being said. However, images are being broken down on the screen. They are shown in detail and complexity . They are being zoomed in and shown the little details and how mathematical figures are used to make these animals and things in nature and society. It also shows how the littlest details create the most beautiful masterpieces. Math ratios and numbers are shown when the images are broken down.

 

The beauty of golden ratio

In this website, in ancient architecture the beauty ratio was used. The great pyramids of Giza was used on the basis of the golden ratio. The parathion  has its exterior based on the golden ratio. The width and height of the U.N. building is also based upon this number ratio.

 

Golden ratio in art and architecture

The famous swiss french architect and painter Le Corbusier  was a strong advocate of the golden ration. However, in the beginning, he strongly disliked and had negative connotations about  the use and work of this number. He later used it to help inspire his work. He has a basic interest in forms and structures.

 

Summary

While watching these videos and reading the articles I found every bit of information interesting. My favorite video to watch was the nature by number one. Seeing how the simplest of details was created from math was astounding. Overall the information that arises from fibonacci and his number was very intriguing and I actually found his golden ration was mathematical beauty to be offensive. Beauty is from within not outside appearance,.

SP:#6 Unit K Concept 10: writing a repeating decimal as a rational number using geometric series

 

Unit K Concept 10: writing a repeating decimal as a rational number using geometric series

 

 

 

When doing these problems remember to not worry about the number in front of the decimal right away: forget about it in the beginning. Since it is a 3 digit repeating decimal it goes on top of 1000 making r=1/1000. You solve it and plug it into the formula and one you get your answer you add it to the umber in front which you previously ignored in the beginning.

Fibonacci Beauty Ratio Blog Post (Extra Credit)

 

Fibonacci Beauty Ratio Blog Post (Extra Credit)

 

 

 

 

 

 

The Fibonacci number is 1.618.... and of my group members Viviane was the closet to that number. What we did was measure our "mathematical" beauty with measurements of various body parts.

In essence I don't think its really beauty physically that we measured but the lengths were beautiful numbers. I would say it isn't that valid because various people had numbers close to this but they are all different shapes and sizes , in all beauty isn't just solemnly one thing, in this case the numbers, however this activity proved to be fun and exciting.

Fibonacci Haiku

Love

 

horrible.

 

heartbreaking.

 

It sucks.

 

Ruins your life.

 

Falling in love is dumb.

 

Love will only crush and break your heart.

 

 

 

 

 

http://parkslopestoop.com/wp-content/uploads/sites/4/2013/01/broken-heart.png

SP#5 Unit J Concept 6: Partial Fraction Decomposition with repeated factors

UNIT J CONCEPT 6

PARTIAL DECOMPOSITION WITH REPEATED FACTORS

Problem difficulty 8out of 5! :)

When doing this problem dont forget to factor out the common denominator completely. Also remember that since they are repeated factor that you must count UP for how many times they reoccur. Also remember that you will end up with two three variable systems in which you can solve them. You will be using elimination to solve them. After you get one answer all you have to do in just plug bak in your answer to find the rest.

SP #4 Unit J concept 5:Partial decomposition with distinct factors

Partial Decomposition with distinct factors

PART ONE

PART TWO

PART THREE

PART FOUR

When completing these problems you must be distribute properly and when decomposing remember to factor out the denominator FULLY. You must then separate them and use letter variables instead.Your common demoninator must be made up of the factors you need and you multiply them to the top. Dont forget that every factor it doesnt have must be multiplied. Dont forget once you start crossing off like terms that the x's cancel out. rememeber to set them equal to the same original factor it corresponds too in the original. Finally if your rref doesnt match the original numbers then you made a mistake.

SV#5 Unit J Concepts 3-4 Solving three variable systems using Gaussian Elimination

Please click to view my video here
When watching the video the viewer should pay attention to how i multiplied the first equation  by negative one so that it is switched however when using rref form i have to use the original problem. Also how to find the first zero i may use either the first or second row but to find the second zero i must use row 1 and to find the last zero i must use row 2 to help me. Also to find the stairstep ones i multiply by the inverse of the leading coefficient. We use rref form on our calculator to check if our answers are right. Dont forget to use the ORIGINAL equation and if there is no variable we put a zero. Our answer that is there should match up with what we got.

SV #4 Unit I Concept 2:Graphing Logarithmic functions and identifying parts

Please click to watch my video here

They needs to pay attention to the the asymptote, as X creates a vertical line. Also, they must acknowledge that you have to exponentiate the log in order to solve for the x-intercept. They must know the difference between how to find h, and that it is opposite of what it is in the equation. Lastly, the viewer needs to understand how to plug in points into the calculator and how to use the log base formula. and use Ln when plugging it into the calculator.

SP3:Unit I Concept 1 Graphing functions and identifying x-intercept, y-intercept, asymptotes, domain, range

  Graphing functions and identifying x-intercept, y-intercept, asymptotes, domain, range

1) To solve these problems first you must identify the parts of the equation and label them. Since this is an exponential graph the asymptote is y=k. To find the x intercept you plug in y=0 however you must take notice if the graph will cross the x axis if not there will be none. To find the y intercept we use x=0 and solve. The domain is not restricted so it will be all real numbers, however our range is so it will depend on if the graph is above or below the asymptote.

WPP #6 Unit 1:Concepts 3-5 Compound Interest.

Create your own Playlist on MentorMob!

SV#3 Unit H Concept 7 Finding logs given approximations

Please watch my video by clicking here

SV#3 Unit H Concept 7

Finding logs given approximations

1) In this video we are given a certain set of clues to approximate logs. It is like going on a treasure hunt.However aside from the clues we are given we must add 2 more. they are log base "B" of b equals one because "B" to the first power is "B", and then Log base "B" of 1 equals 0 because "B"  to the 0 power is one. Then we must break apart the numbers UNTIL the number is part of our cues. It is like using a factor tree but in this sense we stop when our number is a clue. Then we expand each log and finally substitute the log for the clue we were given.

2)When attempting this problem we must not forget to add the clues using the properties of logs. Also when breaking it apart make sure once you hit the clue number you stop. Also remember if it is division being used its subtraction and addition is multiplication. When expanding logs remember that each variable must have its own log.

SV#2: Unit G Concepts 1-7 - Finding all parts and graphing a rational function

Please watch my video by clicking here. Thank you.
  Sv #2: Unit G Concepts 1-7 : Finding all parts and graphing a rational function.
1) In this problem we must find all parts and graph a rational function. A rational function has numbers other than zero. With this problem we are given slant asymptotes to find. We can see that there is one because the degree of the first number is ONE bigger on top then the bottom degree. To find it we must use long division. Next we then find the vertical asymptotes by factoring and IF  something cancels it s our hole, the par of the graph that isn't able to be gone through, hence the name the hole. Then we have to find the x and y intercepts as well the the domain of the function which is D.I.V.A.H. we then find other point by hitting trace on our graphing calculators.
2) One thing to remember is when conducting long division we don't use the remainder as part of our answer.Also when finding the x intercepts we set the numerator to because Y=0, but be careful that whatever had been canceled you don't include. When finding the y-intercept, X=0.When finding the limit notation you plug the equation into the calculator and don't forget the parenthesis and then you see whats occurring as you approach that number from the right and left.

SV#1: Unit F Concept 10 - Finding all real and imaginary zeroes of a polynomial

Please watch my video by clicking here 1) In this problem we are given a quadratic that is not factor able and we must find the factors and well as zeroes. To do this first we begin by using Descartes rule of signs. In this method we are able to figure out how many zeroes are real positive and real negative as well as an estimate if there are any imaginary zeroes. After that we then use the rational root theorem Then we just use synthetic division until we are reduced down to a quadratic.We just factor and find the rest of the zeroes

2) The thing we must not forget is that the odd degrees switch signs in Descartes rule of  sings . Also for the p's and q's it is tempting to also include the q's over p's but those will not work. Also remember that if you are not finding a zero hero in the beginning instead of plugging in all the number you may plug it into a calculator and find some zero heroes. Also until it is reduced down to a factor you still have to conduct synthetic division.

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

1) This problem is about graphing polynomials and including the x-intercepts,y-intercept, the zeroes(with their multiplicities) and the end behavior.To start the problem you must first factor the equation out. Then with the answers you get you will be able to sketch the graph.

2) When doing this type of problem you must first remember to factor it all out. Once you get the remaining value you must solve to zero and then you have your zeroes. You must remember that if it has  multiplicity of 1 then it goes through and if it has one of two then it bounces off.The y intercept is gotten by setting all the x's equal to zero(in this case your answer is zero). The end behavior in this case is even positive therefore the graph will face negative when going to the right and left.

WPP#4: Unit E Concept 3 - Maximizing Area

Create your own Playlist on MentorMob!

WPP#3: Unit E Concept 2 - Path of Football (or other object)

Create your own Playlist on MentorMob!

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

1)this is a quadratic in standard form. The standard form is  f(x)=ax^2=bx=c. In order to graph them more sufficiently we must complete the square so that they can be in the parent function form. The graph will include 2 and 4 points:the vertex, the y-intercept, and up to two x-intercepts, as well as one dotted line which s the axis of symmetry

2).Once you have completed the square, to identify the points and intercepts you need to understand how to find them. to find the vertex you must use the equation (h,k) It could be  a maximum or a minimum. The x-intercepts are the solutions. You set the equation equal to zero and then you solve. To find the y intercept you use the standard form of the problem and plug in 0 for x and then solve  Finally the axis of symmetry divides the parabola so you set it up like x=h.

WPP#2: Unit A Concept 7 - Profit, Revenue, Cost

Create your own Playlist on MentorMob!

WPP#1: Unit A Concept 6 - Linear Models

Create your own Playlist on MentorMob!