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Saturday, March 25, 2006

Jefferson's Scribe - Introduction to conics =3

YES I WAS CHOSEN TO BE FRIDAY'S SCRIBE BY NONE OTHER THAT MANNY!!! thanks pal. I don't know why but I'm really pumped on doing the scribe post. Alright its time to get to business shall we? Today was an interesting yet fun class today. we've met a new character in Mr K yesterday. Rurouni Sensei Kuropatwa was his name. (rorouni = wandering samurai. sensei = master/teacher in Japanese). He un sheathed his meter stick Katana blade(katana = Japanese sword) and asked the class what geometric shape it was. "Its a line Mr. K", says the class. And it was. Mr k grabbed his meter stick in the middle and started spinning it around really fast and then asked the class what shaped he was making. "Two cones Mr. K", says the class. And it was. He then took out his favourite cone (you know? the one that sits in the corner?). He then took his blade and sliced the top part off. It was so fast that the class couldn't see it. He then took off the top and told us that the cross view would be a circle. .He the cut the cone diagonally.(the slice was so fast that you couldn’t see it cutting through the cone). And out came a what looked like an oval or an ellipse. Then he cut it again at a steeper angle and out came a parabola. He then drew a diagram of a double napped cone and the cuts he made to it. Then he said that if you were to cut the cone perpendicular to it(vertically) it would make out a hyperbola. So a recap folks:

Circle- Starts a cone and made from a horizontal cut. At cross view it would be seen as a circle
Ellipse - found from cutting a cone in an angle. An ellipse is also a circle that someone sat on.
Parabola- cutting the base of the cone at a steep angle
Hyperbola - perpendicular to base
These are all called degenerates

Sensei K also said that a conic section has 4 ways of cutting. Those were the 4 ways I was mentioning about. He also said that if you also cut parallel to the vertex of the double napped cone it would be called a degenerate circle.(i'm not sure if that's what it's called)

We then had a new dictionary entry

Conics


There are 4 tipes of conic sections

1. Circles
2.Ellipses
3.porabola
4. Hyperbola


The conic section arise by slicing a double napped cone and looking at the cross section

The “Degenerates”: A point horizontal slice through the vertices produces a point, a degenerate circle. A line: A slice along one of the edges produces a line, a degenerate ellipse. A pair of intersecting lines a perpendicular slice through the vertices produces a pair of intersecting lines ; a degenerate hyperbola.
Locus: A fixed point used in generating the locus for a conic section

Directrix: A fixed line used in generating the locuz for a conic section

Locus definition for conic sections:
A locus (set of points) such that the distance from a fixed point(the focus) divided by the distance from a fixed line(the directrix) is constant.

The Circle:

Definition: The locus of points determined by a fixed distance(the radius) and a fixed point(the centre)

Deriving the standard form for the equation of a circle

(line)OP = T [by definition]
Sqr[(x - h)^2+(y - k)^2] = T [distance formula]
(x + h)^2+(y - k)^2 = T^2[square both sides]

The standard form for the equation of a circle.

Examples:

1. Write the equation of a circle with centre (-2, 3) and radius sqr(5)

(x - h)^2 + (y - k)^2 = y^2 h = -2 k = 3 r = sqr(5) (x - (-2))^2 + (y-(3))^2 = (sqr(5))^2 (x+2)^2 + (y- 3 )^2 = 5

2. Find the centre and radius of the circle (x - 3)^2 + (y - 5)^2 = 4

Centre (3, -5) Radius is sqr(4) = 2

3. Find the centre and radius of the circle x^2 + y^2 - 6x + 10y = 0


x^2 - 6x + y^2 + 10y = -9 x^2 - 6x +9 + y^2 +10 +25 = -9 +9 +25 (x-3)^2 + (y+5)^2 = 25
Centre(3, -5) Radius sqr(25)= 5

We also have homework:textbook, page 141 every 3 up to #63
And thus ends my scribe. I'M VERY PROUD OF MY WORK :")!!! well its time to pick monday's scribe 2 weeks from now. AND HIS NAME WILL BE CALVIN !!! Lets all give him a round of applause *applause*

And its time for me to leave. i've got a lot of things to do on my spring break list.

HAVE A NICE SPRING BREAK GUYS!!
YOU TOO MR. K!! =3



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10 Comments:

At 3/25/2006 1:12 PM, Blogger Mr. H said...

As I read your post the song "Them Bones" came to mind. You know the one.... the neck bone is connected to the back bone et al. What an excellent post. Keep up the great work.

Mr. Harbeck
Sargent Park School

 
At 3/25/2006 7:16 PM, Blogger Emile said...

Nice work, Jeff. How many hours do you put into this one?

 
At 3/25/2006 9:30 PM, Blogger calvinw. said...

rawr last name...

 
At 3/25/2006 9:52 PM, Blogger Jefferson said...

This comment has been removed by a blog administrator.

 
At 3/25/2006 10:01 PM, Blogger Jefferson said...

Apologies for the last name, i've spent 3-4 hrs creating the diagrams and typing up the scribe post.i'm pretty proud of my work actually

 
At 3/27/2006 8:52 PM, Blogger Regine said...

holy you-know-what. that's good work of you. actually, awesome work. You are now my rival for this scribe thing ...again. You'll see.hahaha. but seriously ,the time and effort you put into this will be rewarded. and by rewarded i mean i'm actually going to read all of it.haha. fabulous

 
At 4/01/2006 10:06 PM, Blogger mark said...

man jefferson lol...i just looked at this now and im speechless lol. i don't know what our blog is going to look like in the end... but i have a feeling that it will be completely differenft from the begining =)

 
At 4/02/2006 2:07 PM, Blogger Mr. Kuropatwa said...

Jefferson .... WOW!!!

Every time one of my students posts a scribe that I think has pushed the art form (yes, I think you guys have turned it into an art form) to the ultimate extreme, along comes a scribe that simply blows away all others that have come before and sets a new standard for the scribes that follow.

Sensei Jefferson, domo arigato. ;-)

 
At 5/07/2006 8:36 PM, Blogger Mr. H said...

This is hall of fame worthy. This scribe post stuck in my mind when the Hall of Fame went online.



Mr. Harbeck
Sargent Park School

 
At 5/07/2006 8:48 PM, Blogger Mr. Kuropatwa said...

Mr. Harbeck, you're absolutely right! We should probably scan back through this year's blogs for a whole host of worthy inductees that shouldn't be looked over. ;-)

 

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