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Topic: For Those Who Enjoy Math.

Pythagoras
New Member
Member # 7024

posted

Let A,B, and C be the vertices of any triangle with side lengths a,b, and c

a) show that bc cosA + ca cosB + ab cos c= (a^2+b^2+c^3)/2

b) describe the special case that occurs for the right triangle.

Show all your work. I will inform you if you are correct or incorrect. Enjoy!

[ November 11, 2004, 09:18 PM: Message edited by: Pythagoras ]

Posts: 3 | Registered: Nov 2004 | IP: Logged |

fugu13
Member
Member # 2859

posted

*rolls eyes*

Posts: 15770 | Registered: Dec 2001 | IP: Logged |

Tatiana
Member
Member # 6776

posted

I think you have typos in your post. Please edit for accuracy?

Posts: 6246 | Registered: Aug 2004 | IP: Logged |

Pythagoras
New Member
Member # 7024

posted

Certainly.

Posts: 3 | Registered: Nov 2004 | IP: Logged |

Phanto
Member
Member # 5897

posted

: D

SA DS DS MXC

!!!

MAS

[Smile]

Posts: 3060 | Registered: Nov 2003 | IP: Logged |

Pythagoras
New Member
Member # 7024

posted

Since I have no idea what you are trying to articulate, I will simply tell you that no, that is not the answer.

Posts: 3 | Registered: Nov 2004 | IP: Logged |

King of Men
Member
Member # 6684

posted

I shall prove this in several ways.

1) By inspection. We can easily see that.

2) By private communication. See reference [1].

3) By generalisation. The proposition is trivally true for the case of A = 90, B=C=45, a = sqrt(2), b=c=1. Therefore, waving our hands a little, it seems reasonable to assume it true for the general case.

[1] Leon Lederman, private conversation. I did actually meet Lederman (Nobel Prize winner 1988, if you didn't know) the other day. Very funny guy.

Posts: 10645 | Registered: Jul 2004 | IP: Logged |

Phanto
Member
Member # 5897

posted

Actually, I'm right.

Boo,yeah!

Robot, robot, robot -- ya teba lublu!

Posts: 3060 | Registered: Nov 2003 | IP: Logged |

rivka
Member
Member # 4859

posted

Mr. Pythagoras, sir . . . do your own darn homework. [Razz]

Posts: 32919 | Registered: Mar 2003 | IP: Logged |

King of Men
Member
Member # 6684

posted

Incidentally, just from symmetry, I suspect the exponent of the final 'c' should be 2, not 3. And perhaps you swapped two numbers here, so the divisor on the right-hand side should be 3?

Posts: 10645 | Registered: Jul 2004 | IP: Logged |

MEC
Member
Member # 2968

posted

quote:
bc cosA + ca cosB + ab cos c= (a^2+b^2+c^3)/2

do you mean b*c*cosA + c*a*cosB + a*b*cosC ?

Posts: 2489 | Registered: Jan 2002 | IP: Logged |

Dragon
Member
Member # 3670

posted

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mr_porteiro_head
Member
Member # 4644

posted

wibble

Posts: 16551 | Registered: Feb 2003 | IP: Logged |

Jar Head
Member
Member # 7018

posted

Hey can I just send you my log book? Looks like you could make it clear how I can cover 800 miles at 55 in 11 hours.
[No No]

Posts: 117 | Registered: Nov 2004 | IP: Logged |

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