Fibonacci Haiku: Originality

Try.
Write.
It's hard.
New ideas?
Forget about it.
Keep an eye on those syllables!
(Unless you're cheating and using word limit instead.)
Just kidding, it's not technically cheating; it's just taking the easier way out.

How to Draw the Perfect Pinecone: Fibonacci Numbers in Nature

I found this video while looking up Fibonacci and I think it's really neat! This person posts a lot of other math related things too (check out her video on snowflakes if you're looking for something quick to make for the upcoming winter holidays. :D)

SP#5: Unit J Concept 6: Partial Fraction Decomposition (Repeated Factors ver.)

*FYI: The step numbers do not necessarily correlate with the numbers in the image.*

Step 1: Seperate your denominator factors into fractions- in this case, one of the factors is cubed, so when writing the fractions out remember to count up the factors. [1]
Step 2: Find a common denominator. In this case, you simply have to multiply the numerator by the factors that aren't already in the denominator. Then once you've multiplied and FOIL'd all the numbers and letters, set it equal to your original equation.
Step 3: Seperate the like terms into 4 different equations. At this point, you can take out the 'x cubed', 'x squared', and 'x' values and leave just the coefficients. [2]
Step 4: Two of your equations should have 2 terms and the other two should have 4 terms. Take the latter two equations and use elimination to get rid of a term. In this case, I multiplied the purple equation by two, then added it to the other 4 term equation to get rid of the D term. [3a]
Step 5: Now you have a 3 term equation, but no other one lying around ready to use. Add the 2 term equations together to make another 3 term equation. [3b] Use elimination again to get rid of another value- hopefully you should see where I'm going with this. In this case, I multiplied the 3 term equation by 4 to get rid of the C term.
Step 6: Now you have a 2 term equation. Take any one of your first 2 term equations and use elimination again to get rid of a term. In this case, I multiplied the pink equation by 4 to get rid of the B term, leaving me with the A term.
Step 7: Solve for that final term, then back substitute until you have solved for all the terms. That's it, you're done~!

SP#4: Unit J Concept 5: Partial Fraction Decomposition (Distinct Factors ver.)

Step 1: Find a common denominator. In this case, you have to multiply the numerator by the factors that aren't already in the denominator. Then once you've multiplied and FOIL'd all the numbers, add the common terms together.



Step 2: Set the numerators to letter values (in this case, A, B, and C) and do the same factoring and/or FOILing method as before. However, instead of adding the common terms together, set the fractions equal to your answer from Step 1. Then separate the common terms into three equations.



Step 3: Take the coefficients and put then into matrix form. Input the values into your calculator and put it into reduced row echelon form. Finally, take the answer column and put each one over a factor in fraction form. Look familiar? It should, that's the equation we started with.

SV#5: Unit J Concepts 3-4: Solving Matrix Problems

~>To watch my video, click the link here<~

This video will show you how to solve Problem 5 of the DP problems. In order to watch this video, you should probably pay attention to all the negative and positive signs. Check your math often because I tend to trip over my words and might say something incorrect before going back over it.