## Taylor's Polynomials

### Specials

A location for "special" episodes, which are either separate from, or tangent to the series.
Liable to contain more math, hopefully some may act as an instruction guide.

#### 034-SingAlong: "O Factor Tree"

posted Dec 25, 2013, 4:56 AM by Gregory Taylor   [ updated Dec 25, 2013, 5:32 AM ]

 (For Christmas: Dec 25/13)SING-ALONG 03Math-Tans  present...."O Factor Tree"  (*aka "O Tannenbaum"/"O Christmas Tree", August Zarnack/Ernst Anschutz)--------     Glee Version: YouTube Here      Nat King Cole German Version: YouTube Here     Karaoke Version: YouTube Here     Charlie Brown Instrumental Version: YouTube Here    O Factor Tree, O Factor Tree,Thy primes are so amazing.O Factor Tree, O Factor Tree,Thy primes are worth some praising.Not counting one, primes start with two,The rest are odd, but tried and true.O Factor Tree, O Factor Tree,Thy primes are so amazing.O Factor Tree, O Factor Tree,Least common multiple plea.O Factor Tree, O Factor Tree,Great common factors from thee.We find those parts, comparing trees;Venn diagrams help locate these.O Factor Tree, O Factor Tree,Those "common" goals you'll bring me.(Glee version: Primes are not composites...)O Factor Tree, O Factor Tree,Prime Factor-y directing,Your structure, it's, whole number bits,Have primes so worth detecting.Each branching off, each division,Will stop at primes, like Nine-One-One.O Factor Tree, O Factor Tree,Thy primes are so amazing.(Option: Repeat first verse)O Fractal Tree?Previous Years: "A Squared Song"  ;  "Decimal"You can go here to Comment!

#### 033-The Calendar: Around the World

posted Nov 27, 2013, 4:19 AM by Gregory Taylor   [ updated Nov 27, 2013, 12:14 PM ]

#### 032-Para Sings: "Don't Stop With Riemann"

posted Sep 29, 2013, 5:54 AM by Gregory Taylor

 PARA SINGS 12ax2 + bx + c  presents...."Don't Stop With Riemann"  (*aka "Don't Stop Believin'", Journey)--------Official video: Unable to locate (Copyright pull?)Live Band Performance: Vevo here Source Lyrics video: YouTube HereKaraoke version: YouTube HereGlee Lyrics version: YouTube HereKaraoke Glee Version: YouTube Here***Just approach from left,Estimate is low, I guess.We want the area underneath this curve.Just approach from right,Estimate is high, how trite.We want the area underneath this curve.(Instrumental)(Glee option call out: "Riemann!")A manner to approximate?A summation to contemplate!Every trial helps us to refineIt goes on and on and on and on...{Refrain:}Segments, added. Up or down along this curveTheir width we'll narrow, out of sight.Limit's useful, telling us to stop and observeGives us answers which are right!Working with unending sums,Series is what this becomes.Breaking vastness into discrete partsWe'll comprehend.Some see now, some years hence,Some may only grasp a sense!But the learning never ends,It goes on and on and on and on...{Refrain:}Segments, added. Up or down along this curveTheir width we'll narrow, out of sight.Limit's useful, telling us to stop and observeGives us answers which are right!(Instrumental)Don't stop with Riemann,Try some integration!Limits, useful, ohhhhhhh.Don't stop with Riemann,Try some!Limits, useful, ohhhhhhh!(repeating option)Graph pics from this site:http://www2.seminolestate.edu/lvosbury/CalculusI_Folder/RiemannSumDemo.htmExplore with your own sums here:http://www.mathopenref.com/calcriemann.html

#### 031-Para Sings: "When Can We Cancel"

posted Sep 25, 2013, 4:19 AM by Gregory Taylor

 PARA SINGS 11ax2 + bx + c  presents...."When Can We Cancel"  (*aka "With Or Without You", U2)--------Official Music Video:  YouTube HereSource Lyrics Video:  YouTube HereKaraoke version:  YouTube Here***See the fraction on your page,Feel the brain start to engage.But wait. Think through.Factor first, and check the whole,To be common that could be your goal.Yet it comes. This next cue.So can we cancel?When can we cancel?Through it all, steps must equate,Don't try to rush, you won't be late.Yet I'm worried for you.When do you cancel?When can we cancel, ahh...I hear screams:Now can we cancel?!(Instrumental)And it seems to multiplyAnd it seems to multiplyAnd it seems, and it seems,And it seems to multiply...?You're adding here.Missed factors too, let's stop and check.Sub in an x, andSee if it's still true!And it seems to multiplyAnd it seems to multiplyAnd it seems, and it seems,And it seems to multiply!When can we cancel?WHY can we cancel - Aha!Check your schemes,For why things cancel!Soooooo... Ohhhhh.... Knooooow....Why can we cancel?Why can't we cancel, oho!Know the means,For why we cancel,When we will cancel.Ooooooh!(Instrumental)

#### 030-Para Sings: "Matching Fraction"

posted Sep 22, 2013, 5:14 AM by Gregory Taylor   [ updated Sep 22, 2013, 5:20 AM ]

 PARA SINGS 10ax2 + bx + c  presents....(We Can't Find No) "Matching Fraction"  (*aka "Satisfaction", The Rolling Stones)--------Official Video (Extended Live):  YouTube HereSource Lyrics:  YouTube HereKaraoke version:  YouTube Here***[ROOT(2)]:We can't find no... matching fraction.We can't find no... matching fraction.But I try ... and I try ... and I try ... and I try!I can't find one! I can't find one!When I'm wantin' decimals,And that number has no ratio,(And) I'm soundin' so skeptical!About this exact calculation,Supposed to use new classification?I can't let go! Ir-ra-tion-al!Hey hey hey! It's so risque![PI]:We can't find no... matching fraction.We can't find no... matching fraction.But I try ... and I try ... and I try ... and I try!I can't find one! I can't find one!When I'm usin' my circles,And a plan forbids me rounding!First, that is irony!But we, know 2-pi-r, is circumference,That claim is our math decree?I can't let go! Ir-ra-tion-al!Hey hey hey! It's so risque![PHI]:We can't find no... matching fraction.We can't find no... decimal faction.But I try ... and I try ... and I try ... and I try!I just get ones! I can't find one!When I'm seein' symmetry,And I'm hearin' this, "golden ratio",And it's found in Fibonacci!This tells me, maybe better attack, the new technique,Soon you see I'm such, a numbers geek,We must let go! Ir-ra-tion-al!(But) Hey hey hey! It's so risque!We can't find one! We can't find one!We can't find one... ir-ra--tion-al!No matching fraction... no matching fraction... no decimal faction...We can't find one!

#### 029-Para Sings: "Makin' a Graph"

posted Sep 18, 2013, 4:17 AM by Gregory Taylor

#### 028-Uncommon Denominators

posted May 19, 2013, 5:54 AM by Gregory Taylor   [ updated May 19, 2013, 6:17 AM ]

#### 027-ParaB Sings: "Mean"

posted Apr 14, 2013, 7:07 PM by Gregory Taylor   [ updated Apr 14, 2013, 7:23 PM ]

 PARAB SINGS 07(y-k)2 - 4p(x-h) presents...."Mean"  (*aka "Mean",  Taylor Swift)--------Official Video:  YouTube HereLyrics Only Reference:  YouTube HereKaraoke:  YouTube Here***  Mu:                            X-Bar:                          [Verse 1]Mu. Take your sum, divide, and it's the average that you've found, again, say,Mu. If data's equal weight, oh wait, got me worrying about that,Mu. With outliers it fails to be central, skewing me up when I use it,Mu. Picking it's no master plan.Well, mu can bring us down,If one data's too low.So let me show you where we go...[Chorus]Sometimes, you'll see, median can be so pretty,The middle, may not be the same as mean.Sometimes, you'll see, frequency to mode's not tricky,Most often, may not be the same as mean.Why you gotta use the mean?[Verse 2]Mu. Distributions they, maybe be normal, yay, but we've no indication,Mu. It may not be the centre, but still gives us standard deviation.I'll make a histogram, get my bin width right, 'cause I'm worried about skew,Why. Did average let me down again?I'll bet you thought close enough, one value's no big deal.But the mean moves to it now,Past all the rest, oh how surreal,So let me show you where we go...[Chorus]Sometimes, you'll see, median can be so pretty,The middle, may not be the same as mean.Sometimes, you'll see, frequency to mode's not tricky,Most often, may not be the same as mean.Why you gotta use the mean?[Verse 3]And if we compare aggregates as x bar, talking over what's best for you,Break that down to many pieces and, the reverse could be true!Guess what, you've stumbled, right into Simpson's Paradox.Hope you know some weights or you'll be on the rocks.Since all you use is mean.Hope you know when mean...Is a liar!  And pathetic!    And not weighted right,And mean, it's mean,    that mean, I mean... That[Chorus]Sometimes, you'll see, median can be so pretty,The middle, may not be the same as mean.   Yeah!Sometimes, you'll see, frequency to mode's not tricky,Most often, may not be the same as mean.Why you gotta use the mean?Sometimes, you'll see, median can be so pretty,(Why we gotta use the mean?)The middle, may not be the same as mean.(Why we gotta use the mean?)Sometimes, you'll see, frequency to mode's not tricky,(Why we gotta use the mean?)Most often, may not be the same as mean.Why we gotta use the mean?

#### 026-ParaB Sings: "Choosing a Sample"

posted Apr 10, 2013, 8:34 PM by Gregory Taylor   [ updated Apr 10, 2013, 8:41 PM ]

 PARAB SINGS 06(y-k)2 - 4p(x-h) presents...."Choosing a Sample"  (*aka "Eleanor Rigby",  The Beatles)--------Official Video: Found HereLyrics Only Reference: YouTube Here***Ahhh, look at all the ways to sample.Ahhh, look at all the ways to sample!For systematic, pick every Nth, from a list, of the population.Until you're done.Stratified sample, grouping by trait, taking some, from each group, it makes sense.By the percents!All the ways to sample.How do we choose just one?All the ways to sample.How can we be random?For cluster sample, groupings must each represent, from the big, to the small.From some pick all.Multi-stage sample, grouping's the same, represent, but to time, we succumb.From some pick some.All the ways to sample.How do we choose just one?All the ways to sample.How can we be random?Ahhh, look at all the ways to sample.Ahhh, look at all the ways to sample!Convenience sample, see who's around and they'll do, probability's missed.Bias exists.Destructive sample, quality test, now it's gone, and there's fewer to spare. Use it with care.All the ways to sample.    (Ahhh, look at all the ways to sample!)How do we choose just one?All the ways to sample.    (Ahhh, look at all the ways to sample.)Now can you be random?

#### 025-ParaB Sings: "Minor Axis"

posted Apr 7, 2013, 7:01 PM by Gregory Taylor   [ updated Apr 7, 2013, 7:08 PM ]

 PARAB SINGS 05(y-k)2 - 4p(x-h) presents...."Minor Axis"  (*aka "Inner Ninja",         Classified ft. David Myles)--------Official Video: YouTube HereLyrics Only Reference: YouTube Here***(Spoken:)"Conic? You're a conic? Parabolas, those are conics?""Yes, they are a conic."I knew their forms before I graphed them.I saw the planes and where they'd intersect.(Uh) Now I'd pay close attention,(Yeah) Really know these cones,(Uh-huh) You'll learn to graph on sight, given the six unknowns.                                                                           (counts counts)[Verse 1:]Hey yo, I know some sym-metry, is the key.But the minor axis part, it bothers me.'Cause I am musing it's confusing when choosing fits,Though if ellipse is the conic, position your wits.Don't be lost with those axes, major is long,To standard form and, surely you can't go wrong.Two numbers in the bottom, take the biggest,With x, left-right, if y, more height,It's not hard. And I am finding a difference too,To focus you, I don't miss any square root cue.Cause major axis was the plan, we'll use '2a','b' and 'c', featured also, triple play.Now, if a and b were equal,Graphing a circle wouldn't be deceitful,Special case of it, you know the place for it,Set it, or forget it, as proof can make it clear.I knew their forms before I graphed them. (I graphed them.)I saw the planes and where they'd intersect.Now I'd pay close attention, (come on)Really know these cones,You'll learn to graph on sight, given the six unknowns.[Chorus:]Just say,No conic's gonna have me guessing.No conic's looking too profound.No matter what form you're stressing.No stopping me since I've found...The major axis. The minor axis.The major axis. The minor axis.[Verse 2:]Hey yo, I've seen sums but here's subtraction.Both a hyper and bola's my reaction.So is it up and down, or sideways frown,We will check the signs, on each fraction.I'm seeing term positive, that's the major one,Match x or y, then transverse is done.When you box a and b, asymptotes there.Yeah, I sketch my double curve, using due care.(Here we go)I know, I've assumed you knew square root arises,Axis conjugate, had a name. (name)Focus too, used a sum, but those are not surprises,No drama when so much is the same. (same)It's appealing when you prove, to yourself, every move,Like the way parabolas, mean a square's removed,And you (uh) seize on, what puts you at ease onAll the conic (unh) by using good reason.If only one square, parabola (we told ya)Sum means ellipses, and some circles too.Subtract means hyperbola,Such eccentricity!There isn't any more that you can throw at me.[Chorus:](Let me hear you say!)No conic's gonna have me guessing.No conic's looking too profound.No matter what form you're stressing.No conic's getting me unwound. (Say what?)No conic's gonna have me guessing.No conic's looking too profound. (pssh!)No matter what form you're stressing.No stopping me since I've found...The major axis. The minor axis.The major axis. The minor axis.(Break it down!)If only one square, parabola (we told ya)Sum means ellipses, and some circles too.Subtract means hyperbola,Such eccentricity!There isn't any more that you can throw at me.(Spoken:)"Man, that lacked slope!""You bet.""What are you like a third degree function?""Actually a conic is degree two. Where I found... the minor axis."

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