03-08-10
"It is clear that the chief end of mathematical study must be to make the students think."—John Wesley Young
Korpi’s Monday Mail
03-08-10
to
03-12-10
Good morning everyone.
This is the 27th week of school and the second week of the 5th six-weeks grading period.
Here’s this week’s scoop.
Registration for AP exams will is currently underway. This year’s registration is entirely online, although payments must still be made in person to the front office. Parents and students can follow the link on my homepage at www.korpisworld.com or clicking on http://www.totalregistration.net/schools/newbraunfelshs/ap . Registration must be complete by Friday, March 19.
In Precal, on Monday we will have our test over the Law of Sines and the Law of Cosines. On Tuesday we’ll begin our study of conic sections, beginning with circles. On Wednesday and Thursday in class, we’ll be taking a benchmark exam that will count as two daily grades. On Friday we’ll learn about the next conic section, the ellipse.
In Cal AB, we’re reviewing full-time now. AP Review 4 is due Monday, 5 on Tuesday, 6 on Wednesday, 7 on Thursday, and 8 on Friday.
In Cal BC, on Monday we’ll learn the direct and limit comparison tests for series. On Tuesday we’ll learn the Alternating series test and the Ratio and Root test. On Wednesday we’ll review all methods of tests of convergence and go over any questions from the online worksheets. On Thursday and Friday we’ll begin our study of Power Series.
Here’s the scoop around campus this week:
5:00/7:00 Softball vs Roosevelt (JV/V)-Away
6:00 NB Senior Citizens Prom-NBHS Commons Area
8:15-2:30 YLNB Field Trip
9:00 Women’s Golf at Delaware Spring, Burnet
4:30 Varsity Baseball vs Churchill-Away
5:00/7:00 Sub Varsity Baseball vs Churchill (JVb/JV)-Home
JVb Baseball at Smithson Valley Tourney-TBA
JV Baseball at Canyon Tourney-TBA
Tennis at Samuel Clemens Tourney-TBA
9:00 Men’s Golf at Delaware Springs, Burnet
JVb Baseball at Smithson Valley Tourney-TBA
JV Baseball at Canyon Tourney-TBA
Tennis at Samuel Clemens Tourney-TBA
5:00 Girl’s Varsity Soccer vs Johnson-Home
5:00/7:00 Softball vs Reagan-Home
7:00 Boy’s Varsity Soccer vs Johnson-Home
Saturday, March 13
JVb Baseball at Smithson Valley Tourney-TBA
JV Baseball at Canyon Tourney-TBA
Tennis at Samuel Clemens Tourney-TBA
Track at Judson Relays
NB Winterguard Invitational-All Day
9:00am/11:00am Boy’s Sub Varsity Soccer vs Johnson (JVw/JVb)-Home
9:00am Girl’s JV Soccer vs Johnson-Away
And now for a little Mathematical Mirth and Merriment . . .
MATH BIO:
Gabriel
Cramer (1704 – 1752) was a
Swiss mathematician, born in Geneva the son of physician Jean Cramer and Anne
Mallet Cramer. He showed promise in mathematics from an early age. At 18 he
received his doctorate and at 20 he was co-chair of mathematics at Académie de
la Rive (later professor at Geneva). In 1728 he proposed a solution to the St.
Petersburg Paradox that came very close to the concept of expected utility
theory given ten years later by Daniel Bernoulli.
He published his best known work in his forties. This was his treatise on algebraic curves, "Introduction à l'analyse des lignes courbes algébriques", published in 1750. It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position. In this work he also introduced Cramer's rule 1750, a method for the solution of linear equations which revived interest in the use of determinants;
He edited the works of the two elder Bernoullis and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746).
MATH FACT:
Cramer’s paradox:
The Maclaurin-Bézout theorem says that two curves of degree
n always intersect in 
points,
so for example, two cubics, of degree 3 each, would intersect in nine points.
Cramer, however, discovered that a curve of degree n is generally
determined by 
points.
This means a single cubic curve of degree 3 would require 9 points to determine
its unique curve. This means that points
do not always uniquely determine a single curve of degree n, as in the
picture show at right. Therein lies the paradox.
MATH QUOTE:
“... in order that persons who had a taste for these sciences but no Latin could profit.”—Cramer, on why he taught his classes in French rather than the excepted, traditional Latin.
LIMERICK:
On Cramer’s Paradox:
A very smart man from Berlin
Said, “Constructions and Curves are akin.
But some, without doubt
Leave parts of curves out,
While others put extra curves in.