Ms. Liefland @ Harper Junior High: Geometry

Wednesday, January 9, 2013

Geometry - CIRCLES (January)

Circles worksheet Page 1 and 2 (scroll down for answer key) can be downloaded here:

https://dl.dropbox.com/u/40810525/Equations%20of%20Circles.pdf

~Strategies~

To write the equation of a circle in standard form, you need to know two things:
- Center coordinates (h,k)
- Radius

If you know the equation of a circle in standard form, you can learn two things:
- Center coordinates
- Radius

If you know the coordinates of two endpoints of the diameter:
- You can find the distance between them. This would be the diameter.
- If you cut the diameter in half, you get the radius.

If you know the coordinate of a center and a point on the circle:
- You can find the distance between them. This would be the radius.

If a line is tangent to a circle, it means that it just barely "scrapes" the circle so that it touches it in one place. The distance between the tangent line and the center of a circle would be the radius.

2 comments:

AnonymousJanuary 13, 2013 at 5:10 PM
When will you post something for the final?
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UnknownJanuary 13, 2013 at 7:55 PM
We get handouts tomorrow in class and I'll upload the files to here too! Basically if you add the True/False list of topics (also getting a study guide tomorrow) to what we know about triangles that is all the topics for the cumulative test. Tomorrow we are doing a TON of triangles.
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The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.

- G. H. Hardy (1877 - 1947), A Mathematician's Apology, Cambridge University Press, 1994.

"Legend has it that the Pythagorean philosopher Hippasus used geometric methods to demonstrate the irrationality of while at sea and, upon notifying his comrades of his great discovery, was immediately thrown overboard by the fanatic Pythagoreans."

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect but true.

- Bertrand Russell (1872-1970), Autobiography, George Allen and Unwin Ltd, 1967, v1, p158

Gauss: You have no idea how much poetry there is in the calculation of a table of logarithms!

-Jane Muir, Of Men & Numbers, Dover, 1996.