Mr. K taught the class about conic sections by making cuts on a cone with his meter stick. He showed that a horizontal cut forms a circle, an angled cut forms an ellipse, and steeper cuts form a parabola and hyperbola. Later, students constructed parabolas by folding strips of paper and drawing along the creases. This demonstrated properties of the parabola involving points on the curve and its directrix.

1. Conics

2. Morning Class...
Combinatorics Test!
Nothing really in the morning class to scribe about.

3. Afternoon Class...
Mr. K. Showed off his Great Swahord.
[Really just a fancy name of his Meter Stick]

4. First he shows us a horizontal cut to
his Cone. [Most left Image]
Image from:
http://www.brookscole.com/math_d/special_features/ext/internet_activities/wq_algebra/conics/index.htm
He showed us a circle is formed. This is where the
circle comes from.

5. Next he showed us a cut from a bit of an
angle. [Image second from left]
Image from:
http://www.brookscole.com/math_d/special_features/ext/internet_activities/wq_algebra/conics/index.htm
Using this cut an Ellipse is formed.

6. With more of an angle he make yet another cut at the
Cone. [Image second from right]
Image from:
http://www.brookscole.com/math_d/special_features/ext/internet_activities/wq_algebra/conics/index.htm
Now we can see a Parabola is generated.
Remember Grade 11? Yeah its all coming back
to you now eh? Good times, Good times.

7. So how he finally makes a vertical cut.
Stright down cones. [Most Right image]
Image from:
http://www.brookscole.com/math_d/special_features/ext/internet_activities/wq_algebra/conics/index.htm
Great now we have two parabolas? No...its called a
Hyperbola.

8. Somehow the discussion shifts to figure below. Its
suppose to be your burning campsite. You need to
get water and get back there as fast as possible.
[Note: Suppose its all on paper]
Campsite
You
River

9. Campsite
You
River
Well we were told by one of our classmates that the
fastest way from one point to another was a straight
line. However that is really difficult to do with our
current view. You can't get the water and head to the
campsite in a straight line.

10. So if our paper is folded in half or along the quot;riverquot;
line then you could determine the quot;campsitequot; on the
other side of the river. The quot;campsitequot; on the other
side is accesable via straight line.
Campsite
You
River

11. Now we essentially have the answer. If we fold the
paper again along the river then the line below the
river is brought up above the river. Now we have the
shortest way to camp with stopping for water.
Campsite
You
River

12. Mr. then proceeded by giving us each a scrap sheet of
paper. We were about to construct a parabola on
them.
Instructions on Next Slide

13. Make a dot in the lower center part of the sheet. Lable as quot;Fquot;.
Draw about 12 markings on the bottom edge of your sheet.
[Not above the bottom edge but actually on the bottom edge.]
Fold it once for each marking on the bottom. The folds are made by
moving the marking on top of the point quot;Fquot;. Make sure the folds are
sharp, use your finger nail to achieve this.
Draw a line along the inner most creases. When your done you
should have a parabola.

14. So we have somthing that looks like
this...more or less.
F

15. Next we needed to pick
a spot on our prabola
and draw a line from Q
P
there to point F and
straight down
R
F
perpendicular to the
edge of our paper. We
did that three times.
D1 D2 D3

16. We found that:
D P = PF
1
Q
P
D Q = QF
3
R
F
D R = RF
2
I know that mine doesn't look
D1 D2 D3 like the lengths match. This
was not done using the
insturctions he showed us.

17. To be honest i sort of zoned out during this tail end of class.
He explained to use some parts of our parabola . They were the point quot; Fquot;
or our Focus , Vertex , and if i read that correctly its Directrix . I'm sure he
explained more to us but i just can't seem to remember.
Q
P
R
F
D1 D2 D3

18. Fin

19. Wow...that took much longer than expected, and
I'm still not done.
I still have to choose a scribe...
Cheyyt it is i guess...

20. Reminder : Our DEV [Developing Expert Voices]
outlines are due tomorrow if i can recall correctly.
What is that outline you ask? We need to get our
model questions and the units we will be covering
down on paper and handed in tomorrow.
Working by yourself? 4 Questions
Working with a partner? 5 Questions
Working in a group of three? 6 Questions