C-SECTIONS
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- Conic Section, Rhythm Section,
- Intersection of a Plane and Cones: x 2
- The cornerstone of Analytic Geometry!
- If you were the Archimedes,
- You would burn the enemy ships,
- With a parabolic mirror,
- pointed out to sea!
- Or maybe Johannes Kepler,
- Take the data, and it tells ya,
- Orbiting around the sun
- in perfect ellipses.
- Or your name is Alfred Lee
- And you invented LORAN-C
- To track location and the speed.
- At sea apply Hyperbole!
- Or you’re from an ancient clan,
- let’s say Mesopotamian.
- The Circle spins upon a stand,
- A potter’s wheel with clay in hand.
- Conic Section, Rhythm Section,
- Intersection of a Plane and Cones: x 2
- The cornerstone of Analytic Geometry!
- Menaechmus, from Alopeconnesus,
- Had a Delian dilemma,
- Tryin’ to double up
- The volume of a cube!
- Which is how he stumbled
- on the conic sections. Intersections
- of two parabolic sections,
- Answers they exude.
- Given names: Parabola,
- Ellipse, and the Hyperbola,
- from Apollonius of Perga,
- Didn’t name the circle for-ya.
- Circles are a special case:
- Ellipses but with added grace.
- A horizontal plane embrace,
- That’s parallel to the cone base.
- It’s the end of the line.
- I can’t say that we didn’t have a good time.
- But failure’s coming. I predict.
- Our lives aboard a sinking ship.
- Deny it or live in despair.
- Why build a road that goes nowhere?
- I am set, In my ways.
- And there ain’t no future without any change,
- But we both fail in compromise,
- And so it’s time to say goodbye,
- As pain inflames and swells inside,
- I look into your starry eyes.
- And I remember, I am on a lonely spheroid.
- In an elliptical orbit.
- Round a slowly burning focus,
- with its own elliptical locus.
- Though some day it will destroy us,
- we’ve got many days before us.
- And I say, “It is not the time.”
- As we keep on moving oh so quickly through space-time.
- Ambivalent as either point is justified.
- Around with no compulsion to decide.
- I remembered, I was on a lonely spheroid.
- In an elliptical orbit.
- Round a slowly burning focus,
- with its own elliptical locus.
- Though some day it will destroy us,
- we’ve got many days before us.
- Then I realized they never will look to the end,
- No completion, they cycle again and again.
- That’s the way that our lives were intended to be,
- I will focus on you if you’ll focus on me.
- Hold my hand girl and stand on the major axis.
- And we’ll live...
- And we’ll live...
- I remembered, I was on a lonely spheroid.
- In an elliptical orbit.
- Round a slowly burning focus,
- with its own elliptical locus.
- Though some day it will destroy us,
- we’ve got many days before us.
- And I realized they never will look to the end,
- No completion, they cycle again and again.
- That’s the way that our lives were intended to be,
- I will focus on you if you’ll focus on me.
- Hold my hand love and stand on the major axis.
- And we’ll live...elliptically.
- X minus h, Squared.
- over rx squared,
- Plus y minus k squared.
- over ry square-er-d.
- it all equals one!
- Ellipses are one.
- Bet they never told ya,
- It works for Hyperbola,
- The 2 radii,
- rx and ry,
- normally are Real,
- but imagine if you will:
- That Rx Squared OR Ry Squared just happen to be Negative,
- The only way for this to be, a bumble bee, complexity.
- The radius that has an i, don’t get to have no verticii.
- But draw both radii to show, the box that holds the asymptotes,
- now summoning your mortal strength, you’ll find that pesky focal length.
- It’s longer than both radii, when we’re talkin’ Hyperboli!
- Directrix wants you,
- An Equidistant to,
- A Focus, that you find,
- in a lens.
- Directrix wants you,
- An Equidistant to,
- A Focus, that you find,
- In A Radar Dish.
- You move just to escape,
- the space is in the shape
- the shape is in your wake
- and it flows...
- backwards like a wolf
- r animal, parabolic.
- Directrix wants you,
- An Equidistant to,
- A Focus, that you find,
- On a Suspension bridge.
- You move just to escape,
- the space is in the shape
- the shape is in your wake
- and it flows...
- backwards like a wolf
- r animal, parabolic..
- Directrix wants you,
- An Equidistant to,
- A Focus, that you find,
- As you fall back to Earth.
- So it goes,
- and we go with it,
- What else,
- are we to do?
- So it’s time,
- Time to admit it,
- We both know,
- We both know the truth.
- So you made,
- a couple errors,
- with Aristotle,
- and Ptolomey.
- If they knew now,
- All that I found,
- Well I think,
- They would agree.
- So when is the right time to say that you’re wrong?
- The longer you wait is the more damage done.
- For truth is the truth and eventually,
- The truth will remain, for the truth can be seen.
- So we’ll look,
- up to the heavens,
- See what stories,
- They have to tell.
- You can threaten,
- one man to silence.
- But the Heavens!
- Don’t Scare so well!
- So the story,
- of our culture.
- Advances.
- With each new truth.
- So it goes,
- And we go with it.
- What else,
- Are we to do.
- It’s quitting time, at six o’clock.
- A perfect axis, from the bottom to the top.
- Major or Minor there is no distinction,
- ‘cause the focii have merged into one pointy dot.
- At the center of the circular clock.
- No focal length.
- That’s how I feel.
- No focal Strength.
- Is that a Pigeon.
- No focal length.
- That’s how I feel.
- No focal Strength.
- I’m just waiting for the hands to form that sweet diameter.
- Dear god it’s only Twenty-Three past Four!
- I’m feeling Circular!
- No focal length.
- I’m feeling Circular!
- No focal strength.
- I’m feeling Circular!
- No focal length.
- I’m feeling Circular!
- No focal strength.
- a brave semi major axis,
- b the semi minor scared.
- For ellipses also circles,
- area has been declared:
- a times b times pi, for circles
- is of course just pi r squared.
- The same does not hold for circumference
- or perhaps perimeter.
- pi d or 2 pi r for circles,
- but ellipses don’t transfer.
- For Ellipses:
- twice the sum of
- a squared plus b squared, now go,
- take the square root of it all
- and multiply by pi but know,
- that this is just approximation.
- For perfection: Integration.
- Read the newest publication
- by the good Sir Ivory.
- Delivering the information:
- Ellipses rectification.
- Gauss-Kummer’s Series Summation,
- Transforming and reforming and
- Transforming
- the vast hyper-geometry.
- Equation of the circle is a minor adaptation,
- The hypotenuse the radius,
- the legs will give you y and x,
- and stationary is a point,
- the center of the circle,
- just two shift transformations,
- from the origin to anywhere you’re there.
- Inscribed Pythagoras, he’s looking at you, and you must,
- Acknowledge him. Appease him. If you’re lucky you will please him,
- If you don’t he’ll bring you to a world of hyperbolic grieving,
- from which you will never ever go. Though you are always leaving.
- The focal lengths, the axes, semi-major, semi-minor,
- are related to the theorem and there’s no fair theorem finer,
- For Ellipses semi-major is the longest of the trio.
- The focal length is greatest when pertaining to Hyperbolas...you see....
- Inscribed Pythagoras, he’s looking at you, and you must,
- Acknowledge him. Appease him. If you’re lucky you will please him,
- If you don’t he’ll bring you to a world of hyperbolic grieving,
- From which you will never ever go, though you are always leaving.
- Inscribed Pythagoras, he’s looking at you, and you must,
- Acknowledge him. Appease him. If you’re lucky you will please him,
- If you don’t he’ll bring you to a world of hyperbolic grieving,
- From which you will never ever go, though you are always leaving.
- A parabolic mirror in the desert.
- reflects the waves of solar radiation,
- to a tube filled with oil at its focus,
- which then runs to a solar power station.
- The oil in the tube then heats the water,
- which turns a turbine when it turns to steam,
- which spins a coil of wire near some magnets.
- They’re generating electricity.
- It’s AC current!
- They’re generating.
- It’s alternating,
- from the rotating.
- Through the dessert!
- Along the poles,
- and coming in,
- to power our homes.
- An adapter is then plugged into an outlet.
- Electricity flows through a transformer.
- Then it passes through a full-wave rectifier,
- which is really just four diodes in a square.
- The voltage from the wall is still too wavy.
- So before it can be used in a machine,
- a capacitor assists it with the smoothing,
- and now it flows with more consistency.
- It’s DC current!
- I’ll say directly!
- Easy to work with,
- more elementary.
- An adapter,
- is all you need,
- to turn the AC
- into DC.
In the style of:
Gilbert & Sullivan - When I Was A Lad
Gilbert & Sullivan - When I Was A Lad
- Zero, &pi over 6 and more,
- The next one to know is &pi over 4,
- Then &pi over 3 and &pi over 2,
- Are all of the radians I’ll tell to you!
- r is 1, circumference is &pi times 2
- O, thirty, forty-five, sixty, ninety!
- That’s why I love unit circle Trigonometry.
- O, thirty, forty-five, sixty, ninety!
- That’s why I love unit circle Trigonometry.
- The x’s are 1, square root of 3-
- Over 2 horizontal they must be.
- Square root of 2 over 2 and next are,
- One half and zero the stately x.
- Secretly they’re cosine but that’s coming next.
- O, thirty, forty-five, sixty, ninety!
- That’s why I love unit circle Trigonometry.
- O, thirty, forty-five, sixty, ninety!
- That’s why I love unit circle Trigonometry.
- Zero, one half, and square-root of 2-
- Over 2, that’s "y" I’m telling you,
- Square-root of 3 over 2 and 1.
- Sine is the height at any radian,
- The square-root of 4 over 2 is 1!
- O, thirty, forty-five, sixty, ninety!
- That’s why I love unit circle Trigonometry.
- O, thirty, forty-five, sixty, ninety!
- That’s why I love unit circle Trigonometry.
- Now there are three other quadrants to
- The unit circle that is in your view,
- I’m not going to sing them,
- You can work them through,
- And while you are doing that I’ll say to you:
- r COSINE is X!…And r SINE is Y!
- So we all love unit circle Trigonome - tri!
- r COSINE is X!…And r SINE is Y!
- So we all love unit circle Trigonome - tri!