OEF ÏßÐÔ·½³Ì×é --- ½éÉÜ ---

±¾Ä£¿éÄ¿Ç°ÓÐ 19 ¸ö¹ØÓÚÏßÐÔ·½³Ì×éµÄÁ·Ï°.

3¸öÆ¿×Ó

ÓÐ 3 ¸öˮƿ. ÿ¸öÆ¿Àï¸÷ÓжàÉÙË® (ÒÔ cl Ϊµ¥Î»)?

µÈ¾à

ÕÒ³öƽÃæÉϵã p=(x,y) µÄ×ø±êʹµÃ:
  1. p ºÍ q1=(,) µÄ¾àÀëµÈÓÚ p ºÍ q2=(,) µÄ¾àÀë.

  2. p ºÍ r1=(,) µÄ¾àÀëµÈÓÚ p ºÍ r2=(,) µÄ¾àÀë.

4¸öÕûÊý II

ÓÐ 4 ¸öÕûÊý a,b,c,d Âú×ã: ÎÊ ºÍ µÄƽ¾ùÖµÊǶàÉÙ?

4¸öÕûÊý III

Çó 4 ¸öÕûÊý a,b,c,d ʹµÃ:

4¸öÕûÊý

ÓÐ 4 ¸öÕûÊý a,b,c,d Âú×ã: Õâ 4 ¸öÕûÊýµÈÓÚ¶àÉÙ?

Èý½ÇÐεĶ¥µã

ÓÐÒ»¸öƽÃæÈý½ÇÐÎ ABC Âú×ã: ÇóÈý½ÇÐÎ 3 ¸ö¶¥µã A, B, C µÄ×ø±ê?

ÕâÀï¼ÙÉè A=(x1,y1), B=(x2,y2), C=(x3,y3).


3¸öÕûÊý

ÓÐ 3 ¸öÕûÊý a,b,c Âú×ã: Õâ 3 ¸öÕûÊýµÈÓÚ¶àÉÙ?

3ÖÖ½ðÊôµÄºÏ½ð

¹¤³§´Ó 3 ÖÖ½ðÊôÔ­ÁÏÉú²úºÏ½ð. Õâ 3 ÖÖÔ­ÁϵijɷÖÈçÏÂ:

ÀàÐÍÌúÄøÍ­
Ô­ÁÏ A %%%
Ô­ÁÏ B %%%
Ô­ÁÏ C %%%

¹¤³§ÊÕµ½ÁË ¶ÖºÏ½ðµÄ¶¨µ¥, ´ËºÏ½ðÓ¦º¬ % Ìú, % ÄøºÍ % Í­. ÎÊÕâ 3 ÖÖÀàÐ͵ÄÔ­Áϸ÷Ðè¶àÉÙ¶Ö²ÅÄÜÉú²ú³öºÏºõÒªÇóµÄºÏ½ð?


¼¸ºõ¶Ô½ÇÐÎ

ÔÚÒÔϺ¬ ¸ö·½³ÌºÍ ¸öδ֪Á¿ (>3) µÄ·½³Ì×éÀï, È·¶¨½â 1 µÄÖµ.

1 2
2 3
. . .
-1

(½âÊÇ µÄº¯Êý, Óë µÄÆæżÐÔÓйØ.)


Ô²µÄ·½³Ì

ƽÃæÉϵÄÔ²·½³Ì×Ü¿ÉÒÔд³ÉÒÔÏÂÐÎʽ

2+2 = ++,

ÆäÖÐ ,, ÊÇʵÊý.

Çó³ö ,, ÒԵõ½¹ýÏÂÁÐ 3 µãµÄÔ² C µÄ·½³Ì

1=(,) , 2=(,) , 3=(,) .


Æë´Î2x3

ÇóÒÔÏÂÆë´ÎÏßÐÔ·½³Ì×éµÄÒ»¸ö·ÇÁã½â:

= 0     (1)
= 0     (2)

½â x,y,z Ó¦¸ÃÈ¡ÕûÊý.


Æë´Î3x4

ÇóÒÔÏÂÆë´ÎÏßÐÔ·½³Ì×éµÄÒ»¸ö·ÇÁã½â:

= 0     (1)
= 0     (2)
= 0     (3)

½â x,y,z,t Ó¦¸ÃÈ¡ÕûÊý.


Ö±ÏßÏཻ

¿¼ÂÇƽÃæÉÏÓÉÒÔÏ·½³Ì¶¨ÒåµÄÁ½ÌõÖ±Ïß:

x y = , x y = .

ÊÔÈ·¶¨ËüÃǵĽ»µã p=(x,y).


ËıßÐÎ

ÓÐÒ»¸öƽÃæËıßÐÎ, Æ䶥µã ,,,, Âú×ã: Î汧 µÄÖеã (x,y) ÊÇʲô?

6¸öÕûÊý

ÓÐ 6 ¸öÕûÊý ,,,,, Âú×ã: ÎÊ ºÍ µÄƽ¾ùÖµÊǶàÉÙ?

½â 2x2

ÇóÒÔÏ·½³Ì×éµÄ½â.


½â 3x3

ÇóÒÔÏ·½³Ì×éµÄ½â.


Èý½ÇÐη½³Ì×é

ÔÚÒÔϺ¬ ¸ö·½³ÌºÍ ¸öδ֪Á¿ (>3) µÄ·½³Ì×éÀï, È·¶¨½â 1 µÄÖµ.

1+2+3+...+
2+3+...+
. . .
-1+


½âµÄÀàÐÍ

ÓÐÒ»¸öÓÉ ¸öÏßÐÔºÍ ¸ö±äÁ¿×é³ÉµÄÏßÐÔ·½³Ì×é. ÒÔÏÂÐÔÖÊÖÐÄÄЩÊÇÕýÈ·µÄ?
±ðµÄÀàËÆÁ·Ï°:
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