
024  Video Parody Mashup: 3U

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!!

posted Mar 14, 2015, 6:26 PM by Gregory Taylor
[
updated Mar 16, 2015, 10:49 AM
]
(yk)^{2}  4p(xh) presents....
"It's Probability" (*aka "I'm Getting Over You", Carley Rae Jepsen)

***
I wonder at first glance, Will these events have any chance? So we do some trials, get zero to one for each. I ask now, what's defined? I ask now, can these be combined? And it goes awry, can you see the reason why?
When there's chances, for A and B, Don't just multiply them, check if there's dependency! No denying, Since sets get changed, Just keep glancing for the chances data's rearranged,
When finding Probability! That's right, it's Probability! Sit tight, for Probability! In sight's your Probability! Probably. Probably.
Stuck counting real big sets, And intersections they possess, Know B has this chance but I'm seeing A came first. It's more than a bit strange, That I don't think my chances change, But the more we try, No, this you can't deny...
When there's chances, for A and B, Don't just multiply them, check if there's dependency! No denying (no denying), Since sets get changed (since sets get changed), Just keep glancing for the chances data's rearranged,
When finding Probability! That's right, it's Probability! Sit tight, for Probability! In sight's your Probability! Probably. Probably.
That's right, it's Probability. Sit tight, for Probability. Delight in Probability. Possibly.
When there's chances, for A and B, Don't just multiply them, check if there's dependency! No denying (no denying), Since sets get changed (since sets get changed), Just keep glancing for the chances data's rearranged,
When finding Probability.

posted Dec 18, 2014, 5:44 PM by Gregory Taylor
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updated Dec 18, 2014, 6:52 PM
]
(For Christmas: Dec 18/14)
SINGALONG 04
MathTans present....
"Polar Plot" (*aka "Let it Go")

Official Video: Karaoke: THIS PARODY VIDEO: Christmas Lights Version?
Each grid you try, will relate x and y. Rectangular is that graph. The system is Cartesian, It’s the high school epitaph. No other grids considered, they can be denied. Is there nothing else? What will you decide?
Don’t need to know, don’t need to see, Won’t be tested, but math means more, surely! It’s not for grades, there’s no concern... Well, why not learn...
Coordinate angle view. Polar plot, polar plot! Points the way with distance too! I don’t care, math can be for play, r with theta’s fun. The x kinda bothered me anyway.
If r is now our distance, hypotenuse we find. And the theta’s an inverse tan, our slope we’ve reassigned. To convert back, it’s trig we’ll do, with r, cos theta, and sine too, But there’s no need, as by degree... You’ll see!
Radians can be used as well, Polar plot, polar plot! This circle’s magic spell! Functions curl, on this display, r with theta’s fun!
It’s power can be seen for shapes we’ve not applied, Cardioids, Spirals too as Archimedes once described, And don’t stop searching for the ways these points are new! Square root of minus one? Yeah, we can graph that too!
Polar plot, polar plot! No, you won’t find it on your test. Polar plot, polar plot! Please give your marks a rest. Here’s a grid, Shown in a new waaaay! r with theta’s fuuuun. The x kinda bothered me anyway.  Demi Lovato Version:
Official Video: Karaoke: THIS PARODY VIDEO:
Polar plot, polar plot, Coordinate angle view. Polar plot, polar plot, Points the way with distance too.
Each grid you try, will relate x and y, Rectangular is that graph. The system is Cartesian, It’s the high school epitaph. No other grids considered, they can be denied. Is there nothing else? What will you decide?
Don’t need to know, don’t need to see, Won’t be tested, but math means more, surely! It’s not for grades, there’s no concern. Well, why not learn...
Coordinate angle view. Polar plot, polar plot, Points the way with distance too! Functions curl, On this display! Polar plot, polar plot! The x kinda bothered me anyway.
If r is now our distance, hypotenuse we find. And the theta’s an inverse tan, our slope we’ve reassigned. To convert these points right back, trig will be the key, r cos theta, and sine too, but stay with degrees, you’ll see
Polar plot, polar plot! Radians can be used as well, Polar plot, polar plot, This circle’s magic spell! Functions curl, on this display, Polar plot, polar plot! The x kinda bothered me anyway.
Cardioid. Spiral. Graph them upon arrival. Roots with, a minus. See math that’s oh, so timeless. So much you can show!!
Polar plot, polar plot. Coordinate angle view.
Polar plot, polar plot! Points the way with distance too! Functions curl, on this display, Polar plot, polar plot! The x kinda bothered me anyWAY! Background Vocals: Cardioid. Spiral. Graph them upon arrival. POLAR PLOT! Roots with, a minus. See math that’s oh, so timeless. Cardioid. Spiral. Graph them upon arrival. SPIRAL! POLAR PLOT! Roots with, a minus. See math that’s oh, so timeless.
Polar plot.

posted Dec 25, 2013, 4:56 AM by Gregory Taylor
[
updated Dec 25, 2013, 5:32 AM
]
(For Christmas: Dec 25/13)
SINGALONG 03
MathTans present....
"O Factor Tree" (*aka "O Tannenbaum"/"O Christmas Tree", August Zarnack/Ernst Anschutz) O Factor Tree, O Factor Tree, Thy primes are so amazing. O Factor Tree, O Factor Tree, Thy primes are worth some praising.
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; 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 Factory directing, Your structure, it's, whole number bits, Have primes so worth detecting.
Each branching off, each division, O Factor Tree, O Factor Tree, Thy primes are so amazing.
(Option: Repeat first verse)
O Fractal Tree?

posted Nov 27, 2013, 4:19 AM by Gregory Taylor
[
updated Nov 27, 2013, 12:14 PM
]
(For Nov 27/13) THIS IS A TRACKBACK LINK FOR COMMENTS
POLYNOMIALS (WITH TRIG) PRESENT...
Para: Think you know when February 29th, 1600 was?
Quinn: Information! Consider that there's different calendars in use even now, on Earth.
CoTangent: And we need to talk about this today because....?
Para: Hanukkah and American Thanksgiving coincide! Kinda. Details below.
Sexi: We'll build to it. Like always.
1: CHINESE CALENDAR
Para: The Gregorian Calendar  from the Leap Year special  is hardly the only one in use. If you DO use it, you're in the year 2013, continually numbering forwards. But let's instead consider a calendar that uses modular arithmetic!
Cubi: Hey, so, wondering what sort of math that is? Hey, it means at some point we'll stop counting forwards, and cycle back to zero  for example, in mod 5, you would count 0, 1, 2, 3, 4, 0, 1, 2... and so on.
Tangent: Actually, a system of that sort exists in computers  think Y2K. As it is, counting forward by seconds since January 1st, 1970, some electronics may experience memory overflow problems in January 2038.
Quinn: More information! The Chinese Calendar has a cycle of 60 years. Every year is named using two stems. The first component is a celestial stem, chosen from 10 available. The second component is a terrestrial branch  or the 12 animals most people know from place mats in Chinese restaurants.
CoTangent: Wait, 10 and 12 stems would imply a cycle of 120.
Sexi: Aha, nice math. Not the way to count it. As an analogy, consider the celestial stem as numbers and the terrestrial as letters. The counting runs: 1a, 2b, 3c, up to 10j. Then the first resets. 1k. 2l. Then the second resets. 3a. This means it's impossible to have a 2a or a YiZi year.
Para: Which is okay, as half the celestial stems are similar. They use woodfireearthmetalwater, but double them up, separating running water from standing water, and the like.
Cubi: Hey, if you're reading, see if you can mathematically link this sexagenary cycle to "least common multiples"!
Quinn: Information! While a chinese year has twelve months, each year only has up to 355 days. This necessitates a "leap year" every few years, whereby an entire MONTH is tacked onto the calendar.
Para: As a Gregorian reference, the 'Chinese New Year' will always occur between January 21st and February 21st. It's connected to the new moon, but keep an eye out in 2015, when two such moons occur within that time frame.
Sexi: As a final aside, there is some argument about when the Chinese calendar first began. Most give 2637 BC as the date, though the actual use of zodiac animals came later.
ArcTan: All of which seems to have no bearing on American Thanksgiving. What's next?
2: ISLAMIC CALENDAR
Cubi: Hey, here's a calendar that's been with us since 622 AD! Hey, after all, that's when prophet Muhammed established the first capital.
Sexi: This means the Islamic Calendar began after 0 AD, but before the Gregorian reforms of 1582 AD. We're currently living in 1435 Anno Hegirae (AH), and it's been this year since November 3rd, Gregorian.
Quinn: Again information! We're talking about the Lunar Hijiri Calendar in this case. Twelve months, in a year of up to 355 days, not unlike the Chinese. But no leap months. To align with the moon, the calendar adds 11 days over the span of a 30 year cycle.
ArcTan: Why do you keep saying 'Information'?
Quinn: Cubi gets an inflection, why not me?
Para: Of course, the Islamic "day leaps" aren't enough to keep them in line with the Gregorian, so we can't peg dates here, like we did with the Chinese calendar. That said, there's two key events that many Western calendars mark: Ramadan, the name for the ninth month, and EidalAdha, which occurs during the last month of the year.
Tangent: Right, and I can see now how those dates would gradually migrate backwards through the Gregorian calendar. Come to think, won't there eventually come a time when the Islamic and Gregorian calendars identify using the SAME number?
Cubi: Hey, yes, try to figure THAT one out at home!
3: HEBREW CALENDAR
Sexi: Now, the Hebrew or Jewish Calendar is lunisolar, like the Chinese. A year is twelve months of up to 355 days, but again, they add an extra month every few years. That said, their year is not aligned with the Chinese.
Para: Also, their calendar days begin at sunset, like the Islamic calendar. We're currently in year 5774, which has been counting since creation. Or, on comparative Gregorian terms, we're looking at a start in 3760 BC.
Quinn: Information! The Hebrew New Year  Rosh Hashana  is observed in their seventh month. This generally occurs in Gregorian September, depending on the new moon.
ArcTan: Stop saying 'Information'! Also, wait, does that mean the Hebrew calendar updates its year... with the start of the seventh month?
Para: Correct. The start of the religious year  Nisan, the first month  occurs (by Gregorian terms) in March or April. But it remains within the same numbered year as the month previous.
CoTangent: Interesting. So is this where we make the connection between American Thanksgiving and Hanukkah  the latter occurring in the ninth month of the Hebrew Calendar? Or, wait, should I have said Chanuka there...
CoTangent: I thought I was articulating, not spelling.
Sexi: Here's the thing. Chanukkah was declared a Jewish national holiday 2178 years ago, and always occurs on the 25th of Kislev. This year, that's in Gregorian November... meanwhile, American Thanksgiving keeps bouncing around from date to date, depending on Thursdays.
Tangent: As Adam Savage might say, 'There's your problem!'
4: ABOUT AMERICAN THANKSGIVING
Para: Ooh. Do you think we've been confusing anyone by constantly saying "American" Thanksgiving?
Cubi: Hey, who cares, people should know there's a Canadian Thanksgiving too. Hey, did you know, Canadians used to celebrate in early November  but in 1957, Parliament shifted the holiday back into October? Hey, they wanted to avoid it ever being the same week as Remembrance Day... that being November 11th.
Quinn: Infor... hm, fun fact?
ArcTan: Tolerable.
Quinn: American Thanksgiving is presently on the FOURTH Thursday of November. That WASN'T always the case, and moreover, the reason for the change is  Christmas Shopping!!!
CoTangent: What now?
Sexi: American Thanksgiving USED to be on the LAST Thursday of November. But in 1939, that meant November 30th. So, to create an extra week of Christmas shopping, in the hopes of stimulating the economy, Franklin D. Roosevelt said Thanksgiving would be November 23rd, 1939.
Tangent: Um. Wouldn't there end up being the same amount of shopping, it merely gets spread out over five weeks instead of four?
Cubi: Hey, don't think like a mathematician, think like a politician.
Para: The upshot was SOME states celebrated the 23rd, and others the 30th. But it gets better. In 1940, the last Thursday and the fourth Thursday were both November 28th. Yet Roosevelt declared Thanksgiving would be the 21st!
ArcTan: Let's go back to talking about global calendars, that made more sense.
Cubi: Hey, it's fine, in 1941 the House put forth a law to say the LAST Thursday would be Thanksgiving.
Sexi: Of course, the Senate amended it to be the FOURTH Thursday before it passed. Despite that, Texas was still celebrating the LAST Thursday as late as 1956.
Quinn: Why is 1956 important, you ask? Information! 1956 is the time previous to today when Hannukah and Thanksgiving coincided! Both were, by Gregorian Calendar, on November 29th, 1956. Sort of.
Tangent: You mean, assuming you lived in Texas. And are counting based on the first candle of Hannukah, not the second  as we are this year, 2013.
Para: For reference, they also coincided on November 28, 1918 and November 29, 1888. Granted, the candle count varies  remember Hannukah starts with sunset tonight, November 27th, whereas American Thanksgiving is tomorrow.
Sexi: Theoretically, the intersection is due to happen again in 2070. Notably, Chanuka is drifting out of November  that's why the dates are becoming less frequent.
CoTangent: Hm. That was interesting. Thank you.
Quinn: Now, with the Thanksgiving holiday dealt with, can we talk Canadian football to counter "American football"? By which I don't mean soccer.
Quinn: My point exactly.
Sexi: Kind of a one dimensional point, don't you think?
 Information from many websites, though primarily:
http://www.webexhibits.org/calendars/calendarchinese.html http://www.timeanddate.com/calendar/info.html http://www.chabad.org/holidays/chanukah/article_cdo/aid/2343364/jewish/ChanukahandThanksgivingABriefHistory.htm

posted Sep 29, 2013, 5:54 AM by Gregory Taylor
ax^{2} + bx + c presents....
"Don't Stop With Riemann" (*aka "Don't Stop Believin'", Journey)
 Official video: Unable to locate (Copyright pull?) Karaoke version: YouTube Here***
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 refine It goes on and on and on and on...
{Refrain:} Segments, added. Up or down along this curve Their width we'll narrow, out of sight. Limit's useful, telling us to stop and observe Gives us answers which are right!
Working with unending sums,Series is what this becomes. Breaking vastness into discrete parts We'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 curve Their width we'll narrow, out of sight. Limit's useful, telling us to stop and observe Gives us answers which are right!
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: Explore with your own sums here: 
posted Sep 25, 2013, 4:19 AM by Gregory Taylor
ax^{2} + bx + c presents....
"When Can We Cancel" (*aka "With Or Without You", U2) Source Lyrics Video: 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 multiply And it seems to multiply And 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, and See if it's still true!
And it seems to multiply And it seems to multiply And 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)

posted Sep 22, 2013, 5:14 AM by Gregory Taylor
[
updated Sep 22, 2013, 5:20 AM
]
ax^{2} + bx + c presents....
(We Can't Find No) "Matching Fraction" (*aka "Satisfaction", The Rolling Stones)

*** [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! Irrational! 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 2pir, is circumference, That claim is our math decree? I can't let go! Irrational! 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! Irrational! (But) Hey hey hey! It's so risque!
We can't find one! We can't find one! We can't find one... irrational! No matching fraction... no matching fraction... no decimal faction... We can't find one!

