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.
001 - Song PARAdy: "Vertex" 
002 - Song PARAdy: "I Need A Zero" 
003 - Song PARAdy: "Edges are Glorious" 
004 - Lyn/Slope Talk: Exact Values of Fractions
005 - LYN Dance Parody: "Standard Form" 
006 - Singalong Parody: "Decimal" 
007 - Song PARAdy: "Call Her Sextic"          
008 - Song PARAB: "Y-Squared Tiles" 
009 - Song PARAdy: "Polynomials" 
010 - Song PARAB: "The Sine"
011 - Song PARAs: "Cosine It"
012 - Song PARAdy: "Don't Forget Tangent"
013 - Polynomials on Calendar: Leap Years
014 - Song PARAdy: "One Line"
015 - CIRCE Explains: Basic Trig
016 - CIRCE Explains: Reciprocal Trig
017 - CIRCE Explains: Inverse Trig
018 - CIRCE Explains: Older Trig
019 - Song EXPOse: "Merry Old Angle Zone"
020 - Maud on Video: Yes We Khan (Academy)
021 - Song PARAdy: "Exponential"
022 - Song PARAB: "The Medians"
023 - Singalong Parody: "A Squared Song"
024 - Video Parody Mashup: 3U
025 - Song PARAB: "Minor Axis"
026 - Song PARAB: "Choosing A Sample"
027 - Song PARAB: "Mean"
028 - Lyn/Slope Talk: Uncommon Denominators
029 - Song PARA3: "Makin' a Graph"
030 - Song PARAdy: "Matching Fraction"
031 - Song PARAdy: "When Can We Cancel"
032 - Song PARAdy: "Don't Stop With Reimann"
033 - Polynomials on Calendar: Around the World
034 - Singalong Parody: "O Factor Tree"
035 - Singalong Parody: "Polar Plot"
036 - Song PARAB: "It's Probability"
037 - Song PARAB: "They're Fractals"
038 - Song PARAB: "Permute"
039 - Song PARAdy: "MCF 3M Course"
040 - Singalong Parody: "Like a Bell"
041 - Song PARAdy: "Annuities"
042 - Song EXPOse: "Cubic Formula"
043 - Singalong Parody: "Do We Have a Square Here?"
044 - Song PARAB: "We'll Want Stats"
045 - Singalong Parody: "Triangles Rock"
046 - Singalong Parody: "Sequenced"
047 - Singalong Parody: "Three Things of Math"
048 - Singalong Parody: "Solving for Unknowns"
049 - Song PARAdy: "Only When We Train"
050 - Song PARAdy: "I Graph The Line"

050-Song PARAdy: "I Graph The Line"

posted Apr 16, 2021, 8:54 AM by Gregory Taylor

PARA SINGS 16

ax2 + bx + c  presents....

"I Graph The Line"
  (*aka "I Walk The Line", Johnny Cash)

--------


Official recording: YouTube Here
Live video: YouTube Here
Karaoke with Cash audio: YouTube Here
Karaoke without audio: YouTube Here


***

Our correlation, we'll follow with care.
If no outlier, balance all points there.
We may go through points; if not, don't despair.
Now, that sounds fine.
I graph the line.

(Median-Median)
Three sections equal in their size at the outset.
Then medians, for x and y we'll get.
With slope defined, a nudge would be no sweat.
Now, that sounds fine.
I graph the line.

(Least Squares)
Perhaps a mean fit point will help us cope.
Residuals we find, then squares we hope.
Their areas get small, as we find slope.
Now, that sounds fine.
I graph the line.

With any line drawn, finding 'r' won't change.
And it's the same, should x and y exchange.
That coefficient comes from how points are arranged.
Now, that sounds fine.
So graph the line.

(Do your best!)
Our correlation, we'll follow with care.
If no outlier, balance all points there.
We may go through points; if not, don't despair.
Now, that sounds fine.
I graph the line.



049-Song PARAdy: "Only When We Train"

posted Apr 16, 2021, 8:31 AM by Gregory Taylor   [ updated Apr 16, 2021, 8:33 AM ]

PARA SINGS 15

ax2 + bx + c  presents....

"Only When We Train"
  (*aka "Only When It Rains",
     Astrid S & Frank Walker)

--------


Official video: YouTube Here
Frank's channel static version: YouTube Here
Not really karaoke version: YouTube Here


***

Why did I memorize that bad math rule?
Exponents won't distribute, chart's our tool.
Negative root when squaring goes out, that's cool.
Understand meaning, that's where I'm leaning.

New number systems mean perspectives change.
New course means shift our meaning of a "range".
Doing work daily means this all seems less strange.
Practice makes better, be a go-getter.


Since we can grow,
Our skills will get better when we train.
By cramming, you can't know
Enough, we need context in our brains.

So it's only when we train, that we know.
Yes, it's only when we train. That we grow.
Yes, it's only when we train. That we know.
Yes, it's only when we train. That we grow.
Yes, it's only when we--

Someone else may learn at a different speed,
Our backgrounds and course choices count, indeed.
Find out your pace by making the time you need,
Don't think of testing, more personal besting.

Since we can grow,
Our skills will get better when we train.
By cramming, you can't know
Enough, we need context in our brains.

So it's only when we train, that we know.
Yes, it's only when we train. That we grow.
Yes, it's only when we train. That we know.
Yes, it's only when we train. That we grow.

'Cause it's only when we train, that we know.
Yes, it's only when we train. That we grow.
Yes, it's only when we train. That we know.
Yes, it's only when we train. That we grow.

Yes you, will grow,
Your skills will get better as you train.
By cramming, we can't know
Enough, you need context in your brain.

And that's only once you've trained.


048 - SingAlong: "Solving for Unknowns"

posted Dec 25, 2020, 5:23 AM by Gregory Taylor   [ updated Dec 25, 2020, 8:09 PM ]

SING-ALONG 10

Math-Tans  present....

"Solving for Unknowns"
     (*aka "Into the Unknown", from "Frozen II")

--------
     Original by Kristen Anderson-Lopez and Robert Lopez; sung by Idina Menzel.
     Parody Recorded (for play during Covid) : YouTube Here
     Karaoke used from Kristen Ryan : YouTube Here


xxxx, yyyy, zzzz

I could fear you. But no way.

Equation systems, cause no dismay.

We have substitution, if we simply rearrange,

Or a graph’s an option, and we shouldn’t find that strange, no.

Whoa.

There’s one more choice, elimination is its name

And if I scale up, which I might, we’ll still use it with planes.

Row reduce our matrices, the form is echelon

I’m sorry nth dimension, but your mystery is gone.


We’ve found us an answer, this system’s been addressed

We have made a point of checking, now we’ll have no stress,

Solving for unknowns

Solve for the unknowns

Solve all the unknowns

(Ohhh. Ohhh.)

What did we find? If no solution, don’t you shake,

Do not fear double checking, maybe fixing some mistake.

Yet inconsistent systems, they will have no point to spot.

We might get cross, but independent they are not.


Every way’s another outcome, as dependent systems grow,

Since their set is infinite as we can show,

Solving for unknowns

Solve for the unknowns

Solve all the unknowns

(Ohhh)

Sooooo,

Rectangular?

Parametric?

May be polar?

Make that graph quick!

Ohhhhhh. (Ohhh.)

Ohhhhhh. (Ohhh.)

Whoa, x. Whoa, y. Whoa, z.
Whooooa.

What are your answers?

No need to postpone,

How did you follow through,

Solving for unknowns!

{Whew.}




047 - SingAlong: "Three Things of Math"

posted Dec 25, 2019, 4:15 AM by Gregory Taylor   [ updated Apr 16, 2021, 7:36 AM ]

SING-ALONG 09

Math-Tans  present....

"Three Things of Math"
     (*aka "(We Three Things Are Math) Superstars")
     (*aka "We Three Kings of Orient Are", originally "Three Kings of Orient")

--------
     Original Lyrics and Music by John Henry Hopkins Jr. in 1857.
     Karaoke with low vocals: YouTube Here
     Celebrity Version: YouTube Here
     Celebrity Version with different last verse: YouTube Here

We three things are math superstars,
Look like lines or maybe we're bars.
Math notation, brings salvation,
We're your straight avatars.

[chorus:]
Oooh, overline or vinculum,
Fraction bar at minimum,
Absolutely, valued truly,
Guides in math curriculum.

One symbol is all I can claim,
Overline or macron's my name.
Complement or mean event or
Conjugate are my game.

[chorus:]
Oooh, overline or vinculum,
Fraction bar at minimum,
Absolutely, valued truly,
Guides in math curriculum.

Vinculum appears everywhere,
Line segments and roots need my care.
Long division, or precision,
Don't round off, repeat there.

[chorus:]
Oooh, overline or vinculum,
Fraction bar at minimum,
Absolutely, valued truly,
Guides in math curriculum.

Fraction bar's in vinculum's class,
Group my top, then bottom en masse.
The obelus, tries to tell us,
Dividing happens last.

[chorus:]
Oooh, overline or vinculum,
Fraction bar at minimum,
Absolutely, valued truly,
Guides in math curriculum.

Absolute value bars exist.
Vertical, so not on this list.
Learn of more things, learn of math things,
Symbols others have missed.

[chorus:]
Oooh, overline or vinculum,
Fraction bar at minimum,
Absolutely, valued truly,
Guides in math curriculum.

046 - SingAlong: "Sequenced"

posted Dec 25, 2018, 6:00 AM by Gregory Taylor   [ updated Dec 25, 2018, 12:15 PM ]

SING-ALONG 08

Math-Tans  present....

"Sequenced"
     (*aka "Sleigh Ride")

--------
     Instrumental by Leroy Anderson (1948): YouTube Here
     Lyrics by Mitchell Parish (1949), as sung by Johnny Mathis: YouTube Here
     Mini-Lyric version sung by Pentatonix: YouTube Here
     Mp3 Big Band Instrumental Version: Found Here


VERSES FOLLOW RONDO FORM:  A B A' C A" B A:

Right here there's discrete values called terms all ordered for you.
Come on, it's time for wonders with a sequence of numbers or two.
Does every hailstone sequence end "four two one"? We've no clue.
Come on, it's time for wonders with a sequence of numbers or two.

Two four six, two four eight, two four sixteen finds,
Plus, times, and squared kinds.
We're counting in these ways to train our minds.
Three six nine, three six twelve, three nine eighty-one,
New start means new fun.
We're counting so quick, there's no trick, you can pick when to be done.

Formulas used may vary, so please be wary and know,
Recursion can with some care, give the start along with where to go.
Convergence also exists, since limits persist, it's true.
Come on, it's time for wonders with a sequence of numbers or two.


With a one, one, two, three,
five, eight, thirteen, twenty-one,
You know that the Fibonacci sequence has begun.

But the Lucas sequence
Has the same rule, start with "2, 1" to try.
Golden ratio still applies,
In math that's phi. Phi, phi, phi.


Figurate sequences
Represent geometry.
One has triangles that need no trigonometry.

Then these figurate terms, may appear too
In Pascal's triangle.
Yang Hui drew that first, in China,
There's a lot there to untangle...
Yang Hui drew that first, in China,
There's a lot there to untangle!


Right here there's discrete values called terms all ordered for you.
Come on, it's time for wonders with a sequence of numbers or two.
Does every hailstone sequence end "four two one"? We've no clue.
Come on, it's time for wonders with a sequence of numbers or two.

Two four six, two four eight, two four sixteen finds,
Plus, times, and squared kinds.
We're counting in these ways to train our minds.
Three six nine, three six twelve, three nine eighty-one,
New start means new fun.
We're counting so quick, there's no trick, you can pick when to be done.


(Lyrical conclusion:)
Formulas used may vary, so please be wary and know,
Recursion can with some care, give the start along with where to go.
Convergence also exists, since limits persist, it's true.
Come on, it's time for wonders with a sequence of numbers or two.
Oh yes, it's time for wonders, with a sequence of numbers, or two.

(Instrumental conclusion:)
Formulas used may vary, so please be wary and know,
Recursion can with some care, give the start along with where to go.
Convergence also exists, since limits persist, it's true.
Come on, it's time for wonders, it's time for wonders, it's time for wonders,
it's time for wonders, yes time for wonders, oh time for wonders...
With MAAAAATH. Sequenced.




045-SingAlong: "Triangles Rock"

posted Dec 25, 2017, 6:44 PM by Gregory Taylor   [ updated Dec 25, 2017, 7:18 PM ]

SING-ALONG 07

Math-Tans  present....

"Triangles Rock"
     (*aka "Jingle Bell Rock")

--------
     Original Bobby Helms carol: YouTube Here
     Karaoke Version: YouTube Here

Triangles, triangles,
triangles rock.
Three sides around
means three angles found.
Acute or obtuse,
when no angle’s right.
Classifying there’s
black and white.

Triangles, triangles,
triangles rock.
Three sides equal?
Equilateral.
Two sides, hey that’s called
An isosceles.
Scalene’s last to tease.

Orthocentre’s
an adventure,
Displayed with altitudes.
Try some centroids,
Balance employed,
We use medians
As their preludes.

Incenter, circle’s in,
bisectors meet.
Circumcentre’s no shock.
There’s more middles,
Euler’s line is so neat.
That’s why triangles rock.

(REPEATS:)
Triangles, triangles,
triangles rock.
Three sides equal?
Equilateral.
Two sides, hey that’s called
An isosceles.
Scalene’s last to tease.

Orthocentre’s
an adventure,
Displayed with altitudes.
Try some centroids,
Balance employed,
We use medians
As their preludes.

Incenter, circle’s in,
bisectors meet.
Circumcentre’s no shock.
There’s more middles,
Euler’s line is so neat.
That’s why triangles,
Sum 1-8-0 rules,
That’s why triangles rock!




044-Song ParaB: "We'll Want Stats"

posted Jul 22, 2017, 1:23 PM by Gregory Taylor   [ updated Jul 24, 2017, 6:16 AM ]

PARAB SINGS 11

(y-k)2 - 4p(x-h)
 presents....

"We'll Want Stats"
  (*aka "I Want You", Savage Garden)

--------

An Official Video: YouTube Here
Source Lyrics Reference: YouTube Here
The JoJo Part 4 Ending: YouTube Here
This Song Parody: YouTube Here

***

Any time we need to count the ways
You can win a prize,
Or we are reading some essays
Where their data lies,
You should build a tree, or use Venn, so then
your math will look fine, and
we can show off your diploma.

Soon you want the web to explain,
Bias is a fright,
So check the numbers again,
You might have insight, as
To the graphs, and the source and the days,
For the sample that they drew,
Do your search terms control you?

Let’s check error margins closer
Let’s count to numbers much higher
You’ll see much more all around you
(Let’s) manage data.

[chorus:]
Ooh, we’ll want Stats
I don’t know if you’ll heed Stats
But, ooh, I’m dying to find out.
Ooh, we’ll want Stats
I sure know that you’ll need Stats
And, ooh, I’m trying to find doubt.


Normal distribution is pervasive
What does that mean,
The median is on report cards
So have you seen,
a percentile, or modes for fashion and more,
Now is this warranty poor?
Make your argument persuasive.

Roll a seven in this game we play,
which is in-dep-endent of what happened yesterday,
Classify by taking, our math symbols from the words,
As the polls get absurd, aren’t they checking
Who was voting last election?

Let’s check error margins closer
Let’s count to numbers much higher
You’ll see much more all around you
(Let’s) manage data.

[chorus:]
Ooh, we’ll want Stats
I don’t know if you’ll heed Stats
But, ooh, I’m dying to find out.
Ooh, we’ll want Stats
I sure know that you’ll need Stats
And, ooh, I’m trying to find doubt.

Oooh, yeah Stats. Oooh, yeah Stats.

Any time we need to count the ways
You can be surprised,
Or we are reading some essays
Where data’s disguised,
You should build a tree,
Or use Venn, so then
your math will look fine.
Make your arguments persuasive.

Roll a seven playing in this game,
which is in-dep-endent if it happens again,
Classify by taking,
our math symbols from the words,
with the poll, for the sample that they drew.
Don’t let search terms confuse you.

[chorus:]
Ooh, we’ll want Stats
I don’t know if you’ll heed Stats
But, ooh, I’m dying to find out.
Ooh, we’ll want Stats
I sure know that you’ll need Stats
And, ooh, I’m trying to find doubt.
So can we find doubt?

(Probability, Statistics.)
(Probability, Statistics.)


[chorus x2:]
Ooh, we’ll want Stats
I don’t know if you’ll heed Stats
But, ooh, I’m dying to find out.
Ooh, we’ll want Stats
I sure know that you’ll need Stats
And, ooh, I’m trying to find doubt.

Ooh, we’ll want Stats
I don’t know if you’ll heed Stats
But, ooh, I’m dying to find out.
 (I hope we’ll find out.)
Ooh, we’ll want Stats
I sure know that you’ll need Stats
 (I’m here to find out.)
And, ooh, I’m trying to find doubt.

043- SingAlong: "Do We Have a Square Here?"

posted Dec 24, 2016, 2:05 PM by Gregory Taylor   [ updated Dec 24, 2016, 2:39 PM ]

SING-ALONG 06

Math-Tans  present....

"Do We Have a Square Here?"
     (*aka "Do You Hear What I Hear?")

--------
     VIDEO OF THIS PARODY: YouTube Here
     Original carol from 1962: YouTube Here (call/response)
     Carrie Underwood version: YouTube Here (w/ instrumental break)

Shape has four sides, diagonals tease.
Do we see a square here? (Do we see a square here?)
Diagonals cross, at ninety.
Do we see a square here? (Do we see a square here?)
Maybe, don’t know. Though that angle’s right,
Could be rhombus, or merely kite.
Could be rhombus, or merely kite.


Here’s another quad, with attempts to please.
Do we have a square here? (Do we have a square here?)
There’s diagonals, equal length.
Do we have a square here? (Do we have a square here?)
Isos-celes trapezoid maybe?
Rectangle? No square guarantee.
Rectangle? No square guarantee.


Quadrilaterals we now find with ease.
Do we know our square yet? (Do we know our square yet?)
Here’s diagonals, bisecting.
Do we know our square yet? (Do we know our square yet?)
That cut, it shows, parallelogram,
We’d need more to say for certain.
We’d need more to say for certain.


(Key Change)
Equal lengths, bisect, at ninety degrees.
Testing for our square here! (Testing for our square here!)
All three things, diagonals bring.
Testing for our square here! (Testing for our square here!)
It’s found, and with, root two in hindsight,
Our regular quad’s come to light.
Our regular quad’s come to light.
(Do we have a square here?)


Previous XMas Specials:


042 - Song EXPOse: "Cubic Formula"

posted Dec 22, 2016, 11:46 AM by Gregory Taylor

EXPONA SINGS 02

abx + c  presents....

"Cubic Formula"
  (*aka "I Will Follow Him", Sister Act)

--------

Song in Context (end of movie):  YouTube Here
Karaoke Version: YouTube Here

This Cubic Song Parody:  YouTube Here
About Using the Formula: Blog Post Here

*****

Start with b times c.
It’s on six a-squared, now minus d...
On 2a, then minus b-cubed
On twenty-seven with a-cubed.
Let’s call that q? Agreed.

Take cube root of q -
as ADDED inside of this square root...
q squared, once it’s summed to this cube:
c on 3a, minus squared-b
on 9 squared-a’s!

We’re nearly half-waaaaaay!
TEMPO CHANGE

That square root, you ADDED, we’ll use it,
But now we will SUBTRACT it, still from q, cube root too!

(SOLO:)
This gives two numbers.
Kind of six... look, sum the cubes you know.
Then minus b on 3 with a,
We’ll set that to x and hurray! Wait, what was q?

(We’ll get it, we’ll get it)

We took b times c
   
(DUET: B times C!)
It’s on six a-squared, now minus d   (Oooh ooh!)
On 2a, then minus b-cubed   (B Cubed?!)
On twenty seven with a-cubed.
That we called q!
Used four times, it’s true!

(SOLO2:)
Whoa, yeah! Oh yes, solve cubics!
(Degree three!)
Four coefficients!
(Too much!)
Imaginary answers!
(So complex!)
You’ll wish you’d learned to factor!


That square root, you ADDED, we’ll use it,
But now we will SUBTRACT it, still from q, cube root too!
Gives numbers, so get their sum, minus b, on 3a,
Set that to x at leisure, or never, whateverrrr...

If you think that’s only one x,
Remember cube roots of complex!
Gives us all three!
All three solutiooooooons!



041 - Song PARAdy: "Annuities"

posted Dec 20, 2016, 1:18 PM by Gregory Taylor   [ updated Dec 20, 2016, 1:23 PM ]

PARA SINGS 14

ax2 + bx + c  presents....

"Annuities"
  (*aka "It's Raining Men", Weather Girls)
  (*BONUS: Geri Halliwell version)

--------

Official video: YouTube Here
Karaoke version: YouTube Here

Halliwell version lyrics: YouTube Here
Halliwell Karaoke version: YouTube Here


***

Hi - Hi!
Here’s your finance strand - Uh-huh.
And have we got maaaath for you - You better listen!
Get ready, all you interest fans,
And leave simple interest alone. - Alright!

A geometric sequence. - Geo sequence!
Has compound interest grow.  - Grow how, curl?
That exponential curve says, - What's curving now?
We can make lots of dough. - We better invest, yup
Yet to pay more than one time, in perpetuity,
And to sum up that sequence means,
We’ll get an annuity! (Get an annuity!)

Annuities! They use series’, annuities! Yes please!
I’m gonna pay out, with many intervals set,
And hope it keeps me out of debt!

Annuities! They use series’, annuities! Use your expertise!
Years? Months? Quarterly?
Change your ’n’ and then you’ll see!

Now in certain cultures,
This interest is an issue.
And so no investing,
But the math we can continue.
There are formulas here,
And rearranged or not,
You use them or T-V-M apps,
To find what sum we’ve got!

Annuities! They use series’, annuities! Yes please!
Annuities! They use series’, annuities! Yes pleeeeeease!

Watch out for the ann-u-i-ty due, and mortgages too,
Or-din-ar-y simple went unsaid,
But use your apps to work ahead. (But use your apps to work...)

Now in certain cultures, such interest is an issue.
And so no investing, but the math we can continue.
There are formulas here, and rearranged or not,
You use them or T-V-M apps, to find what sum we’ve got!
Oh, annuities! Yeah!

A geometric sequence.
Has compound interest grow.
That exponential curve says...
We can make lots of dough.
Yet to pay more than one time, in perpetuity,
And to sum up that sequence means,
We’ll get an annuity! (Get an annuity!)

Annuities! They use series’, annuities! Yes please!
Annuities! They use series’, annuities! Yes please!
Annuities! They use series’, oh whoa whoa - Annuities!


BONUS Gei Halliwell Version:

A geometric sequence. Has compound interest grow.
That exponential curve says, we can make lots of dough.
Yet to pay more than one time, in perpetuity,
And to sum up that sequence means,
We’ll get an annuity!
Annuities! They use series’, annuities! Yes please!
Annuities! They use series’, annuities! Yes please!

A geometric sequence. Has compound interest grow.
That exponential curve says, we can make lots of dough.
Yet to pay more than one time, in perpetuity,
And to sum up that sequence means,
We’ll get an annuity!
Annuities! They use series’, annuities! Yes please!

I’m gonna pay out, with many intervals set,
And hope it keeps me out of debt!

Annuities! They use series’, annuities! Use your expertise!
Years? Months? Quarterly?
Change your ’n’ and then you’ll see!

Now in certain cultures, this interest is an issue.
And so no investing, but the math we can continue.
There are formulas here, and rearranged or not,
You use them or T-V-M apps, to find what sum we’ve got!
Annuities! Go start saving net pay. I know you need to.

Watch out for the ann-u-i-ty due, and mortgages too,
Or-din-ar-y simple went unsaid,
But use your apps to work ahead.
(but use your apps to work)

Annuities! They use series’, annuities! Yes please!
Annuities! They use series’, annuities! Yes please!
Annuities! They use series’, annuities! Yes please!
(Repeat as needed)


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