001  Song PARAdy: "Vertex"
024  Video Parody Mashup: 3U
 
posted Dec 25, 2018, 6:00 AM by Gregory Taylor
[
updated Dec 25, 2018, 12:15 PM
]
SINGALONG 08
MathTans present....
"Sequenced" (*aka "Sleigh Ride")
 Lyrics by Mitchell Parish (1949), as sung by Johnny Mathis: YouTube 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 eightyone, 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, twentyone, 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 eightyone, 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.

posted Dec 25, 2017, 6:44 PM by Gregory Taylor
[
updated Dec 25, 2017, 7:18 PM
]
SINGALONG 07
MathTans present....
"Triangles Rock" (*aka "Jingle Bell Rock")

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, 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 180 rules, That’s why triangles rock!

posted Jul 22, 2017, 1:23 PM by Gregory Taylor
[
updated Jul 24, 2017, 6:16 AM
]
(yk)^{2}  4p(xh) presents....
"We'll Want Stats" (*aka "I Want You", Savage Garden)

***
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 independent 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 independent 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.

posted Dec 24, 2016, 2:05 PM by Gregory Taylor
[
updated Dec 24, 2016, 2:39 PM
]
SINGALONG 06
MathTans present....
"Do We Have a Square Here?" (*aka "Do You Hear What I Hear?")
 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?) Isosceles 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?)

posted Dec 22, 2016, 11:46 AM by Gregory Taylor
ab^{x} + c presents....
"Cubic Formula" (*aka "I Will Follow Him", Sister Act)

*****
Start with b times c. It’s on six asquared, now minus d... On 2a, then minus bcubed On twentyseven with acubed. 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 squaredb on 9 squareda’s!
We’re nearly halfwaaaaaay!
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 asquared, now minus d (Oooh ooh!) On 2a, then minus bcubed (B Cubed?!) On twenty seven with acubed. 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!

posted Dec 20, 2016, 1:18 PM by Gregory Taylor
[
updated Dec 20, 2016, 1:23 PM
]
ax^{2} + bx + c presents....
"Annuities" (*aka "It's Raining Men", Weather Girls) (*BONUS: Geri Halliwell version)
 ***
Hi  Hi! Here’s your finance strand  Uhhuh. 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!
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 TVM 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 annuity due, and mortgages too, Ordinary 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 TVM 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 TVM apps, to find what sum we’ve got! Annuities! Go start saving net pay. I know you need to.
Watch out for the annuity due, and mortgages too, Ordinary 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)

posted Dec 24, 2015, 5:34 AM by Gregory Taylor
[
updated Dec 24, 2015, 5:36 AM
]
SINGALONG 05
MathTans present....
"Like a Bell (Canonical), in Stats" (*aka "Pachelbel's Canon in D")

(Bar 1: Bass Line Throughout) Distribution, Bell curve nickname. Distribution, Gaussian fame. Distribution, Bell curve nickname. Distribution, Gaussian fame.
(Bar 5: Entry) Normal curve here, Symmetry’s clear. Normal curve here, Symmetry’s clear.
(Bar 13:) Calculate the mean, that’s mu, And variance, that’s sigma squared, too. Calculate the mean, that’s mu, And variance, that’s sigma squared, too.
(Bar 21:) Now here’s the zscore. How far we’ll be, In standard deviations from the centre with symmetry. Now here’s the zscore. How far we’ll be, In standard deviations from the centre with symmetry.
Range for zscores: Three left, three right. Subtract the mean, divide by sigma, Standardizing’s insight.
Range for zscores: Three left, three right. Subtract the mean, divide by sigma, Standardizing’s insight.
(Bar 37: Familiar Melody) Sixty Eight Percent If data’s one zscore out, Ninety Five Percent If data’s two zscores out, NineNine Point Seven, For data three zscores out, Leads to percentiles Of that there can be no doubt!
Sixty Eight Percent If data’s one zscore out, Ninety Five Percent If data’s two zscores out, NineNine Point Seven, For data three zscores out, Leads to percentiles Of that there can be no doubt!
(Repeats as often as you like) (Somewhere after bar 50:) e, as base declared (as base declared) Needs minus point 5, x squared All divided by (divided by) Square root of two pi
e, as base declared (as base declared) Needs minus point 5, x squared All divided by (divided by) Square root of two pi
(Inexplicably at the end:) Normal curve here, Symmetry’s clear. Normal curve here, Symmetry’s oh so clear.
Previous XMas Specials:

posted Jun 27, 2015, 6:18 AM by Gregory Taylor
[
updated Jun 27, 2015, 6:35 AM
]
(barely feat. Expona) ax^{2} + bx + c presents....
"MCF 3M Course" (*aka "Pop Music 101", Marianas Trench) Amyte Piano Cover for Karaoke: YouTube Here***
MCF 3M Course Has functions at it’s source That’s a special relation So let’s learn, notation.
A line has range and domain Those values we obtain And then in the same vein SWAP... Into quadratics.
[STRAND 1] There’s our parabola, Symmetry when we draw The quadratic formula (yeah) I love that (yeah) for solving
Bsquared minus 4ac The discriminant’s that easy Don’t forget the vertex form To give you the steps to transform
Three strands, nine expectations, Watch the order of operations, Practice those applications... Functions galore!
Now here’s the ones you should quote: The xsquared turns around we note, Exponent x means asymptote, Then sin(x), sin(x), sin(x), sin(x), sin(x)
Patterns can make this more clear, Differences, ratios appear. Work hard, right through ‘till end of year, xsquared, exponents and sine x xsquared, exponents and sine x
[STRAND 2] Sine graph looks like a wave Period we will crave Amplitude, axis too (Phase shift out of the blue)
If we model x as time These circles are so sublime Round and Round (yay! whoa!) ... oh yeah.
Then there’s cos and tan, Triangles need a plan. Proportions? Sine law then. If not we’ll  need  cosine  law. (Tangent’s slope)
Three strands, nine expectations, Watch the order of operations, Practice those applications. (Don’t forget  functions are relations!)
Whoa! Now here’s the ones you should quote: The xsquared turns around we note, Exponent x means asymptote, Then sin(x), sin(x), sin(x), sin(x), sin(x)
Patterns can make this more clear, Differences, ratios appear. Work hard, right through ‘till end of year, xsquared, exponents and sine x xsquared, exponents and sine x
[STRAND 3] There are exponent laws we can use. There are exponent laws we can use. There are exponent laws we can use. IF we keep the SAME BASE.
The base is, the value, that gives us, Growth or decay. (Yup) We use percents, and as you sketch, Yintercept, relates to stretch.
[Expona Adds:] Quick now, TVM app! Interest compounds, annuities that switch the formula map and get us to calculate... (CA$H MONEY!)
FFFFunctions galore!
Now here’s the ones you should quote: The xsquared turns around we note, Exponent x means asymptote, Then sin(x), sin(x), sin(x), sin(x), sin(x)
Patterns can make this more clear, Differences, ratios appear. Work hard, right through ‘till end of year, xsquared, exponents and sine x xsquared, exponents and sine x (Oh. Yeah.)
(..... Graph!)
F of x, use F of x, use (It’s the notation) F of x, use F of x, use it.

posted Jun 21, 2015, 8:03 PM by Gregory Taylor
(yk)^{2}  4p(xh) presents....
"Permute" (*aka "Can't Choose", JRDN ft. Kardinall)

***
(Ooooh. Count up, count up, count up.)
[KARD:] (Woo hoo.) I, can’t choose given infinite replenishment One item I’ve taken, in a bin it is present, But then that option we can still pick, total restart, I’m stayin’ with all A’s, for my password, (that’s) not smart. (Yeah!)
Now pipe down, if the item disappears, Then multiply, factorials, Descending numbers here, but I can’t miss the ranks, Since there’s order to use, So when we work it out (see) I can’t choose. (Woo, woo)
[JRDN:] At a meet yesterday, saw them start to play, and I said, “Nice lineup there.
“Do you know how many ways that there’s a roster for this game for your team, using due care?
Because I mean, positions we see here are clear, I know: “The labels will create order, so now we won’t divide by what you take.” I’m no fool.
{CHORUS:} (FacTorIAl.) You divide who’s left out, that’s the law, that’s the law. I’ll exclaim, (FacTorIAl.) “I’m going to divide, and I did take some, ordering them all...” I can’t choose (can’t choose, can’t choose, can’t choose) Oh, I permute (permute, permute, permute) All these things selected But ranking’s not neglected So I can’t choose (can’t choose, can’t choose, can’t choose) Tell you what, we’ll permute. Bought some fruit last week, and I got a critique. Said, “In listin’ these all, well, can I count the ways with my technique?” And I was told, “These three repeat, orange was used again.” But I said, “Great, so if ordering stays, we divide by six then.” I’m no fool.
{CHORUS:} (FacTorIAl.) You divide copies out, that’s the law, that’s the law. I’ll exclaim, (FacTorIAl.) “I’m going to divide, and I did take some, ordering them all...” I can’t choose (can’t choose, can’t choose, can’t choose) Oh, I permute (permute, permute, permute) All these things selected But ranking’s not neglected So I can’t choose (can’t choose, can’t choose, can’t choose)
It’s a permutation! (Count up, count up, count up) Permutation! (Count up, count up, count up) All these things selected But ranking’s not neglected So I can’t choose (can’t choose, can’t choose, can’t choose) Tell you what, we’ll permute.
[KARD:] (Yeah) Don’t know what to do Thought I had a P not a C, but instead I’m here pickin’ randomly. Yo, I’ll always take this and that, who cares what came last, Yeah, it could’ve been first, that’s how I choose fast. Now I divide two times, both numbers match my all (Ha!) But remember there’s no bins here, close call. (Yep) So I gotta use my head and bring some hope that I won’t arrange everything.
{CHORUS:} I can’t choose (can’t choose, can’t choose, can’t choose) Oh, I permute (permute, permute, permute) All these things selected But ranking’s not neglected So I can’t choose (can’t choose, can’t choose, can’t choose) It’s a permutation! (Count up, count up, count up) Permutation! (Count up, count up, count up) All these things selected But ranking’s not neglected So I can’t choose (can’t choose, can’t choose, can’t choose) Tell you what, we’ll permute.
P, n then r nPr P, n then r nPr P, n then r nPr P, n then r

posted Mar 24, 2015, 6:50 PM by Gregory Taylor
[
updated Mar 24, 2015, 6:51 PM
]
(yk)^{2}  4p(xh) presents....
"They're Fractals" (*aka "I Love It", Icona Pop)

***
I thought that Mandelbrot and Julia were such a yawn, I saw they won't be on the test. I passed, I'm moving on. I now admit, the truth of it, they're more than denouement. I know they won't be on the test. I don't care! They're fractals! Let's all share!
I thought that Mandelbrot and Julia were such a yawn, I saw they won't be on the test. I passed, I'm moving on. I now admit, the truth of it, they're more than denouement. I know they won't be on the test. I don't care! They're fractals! Let's all share!
{Refrain:} You're on a Hilbert curve, I'm in the Koch snowflake, You want Sierpinski cuts, but Cantor sets I make. Your attractor is strange, Weierstrass can bewitch, You're folding dragons up, but I'm done with this pitch. They're fractals!
They're fractals!
I thought that Mandelbrot and Julia were such a yawn, I saw they won't be on the test. I passed, I'm moving on. I now admit, the truth of it, they're more than denouement. I know they won't be on the test. I don't care! They're fractals! Let's all share! These fractals. Hausdorff it. Be aware! They're fractals. Let's all share!
{Refrain:} You're on a Hilbert curve, I'm in the Koch snowflake, You want Sierpinski cuts, but Cantor sets I make. Your attractor is strange, Weierstrass can bewitch, You're folding dragons up, but I'm done with this pitch. Be aware! They're fractals! Let's all share! These fractals. Hausdorff it. Be aware! They're fractals. Let's all share! These fractals. Hausdorff it. Be aware!
They're fractals!!

