The thereom of mean similiarty.

by pythag011, Sep 17, 2008, 12:46 AM

Let's say we have two DIRECTLY(whcih means both clockwise or counterclockwise) similiar triangles. ABC and DEF. Let X be the midpoint of AD, Y be teh midpoint of BE and Z be the midpoint of CF.

Then, XYZ is similiar to ABC and DEF.

This can be very useful.

BTW, to explain DIRECTLY similiar and not directly similiar, these triangles are directly similiar

[geogebra]743d4b453524ba09db74b2b69ec2a5521edab340[/geogebra]

The ones on the left are directly similar. The ones on the right are oppositely similar.

More generaly: Let there be two directly similiar polygons. Then teh polygon formed by their midpoints of corresponding vertices are directly similiar to th epolygons.

Yeah, I know I suck at exlaining things. *sigh*

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Directly similar: If, on a plane, they have the same chirality, they are directly similar.
That is to say if the only tools you need to obtain the two triangles are homothety and rotation
Oppositely similar: If you need to flip the diagram in order to obtain the similarity, they are oppositely similar.
Like you hands... somewhat. Rotate your hands, no matter how hard you try you WON'T MATCH THEM UP.

by james4l, Sep 17, 2008, 1:08 AM

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dude we can like prove this by taking the center of spiral similarity between these two triangles (polygons) and then like use spiral similarity to get the desired direct similarity

by The QuattoMaster 6000, Sep 17, 2008, 3:20 AM

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hello

vectors

by not_trig, Sep 19, 2008, 1:15 AM

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hello spiral similarity

by The QuattoMaster 6000, Sep 19, 2008, 10:51 PM

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bump...
https://artofproblemsolving.com/community/c1352h993021
by Bryan0224, Nov 17, 2024, 1:13 PM
first shout of 2024
by QueenArwen, Nov 12, 2024, 12:04 PM
nice blog
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fantastic blog!!
by lneis1, Jul 8, 2021, 8:03 AM
what a pr0 blog
by centslordm, Jun 24, 2021, 4:34 PM
pythag011 orz
by tigerzhang, Jun 21, 2021, 5:39 PM
greetings
by Kanep, Oct 26, 2020, 12:38 PM
A very fine blog.
by Catoptrics, May 29, 2020, 11:42 PM
this is dead
by fukano_2, May 20, 2020, 10:35 PM
Found this
by Williamgolly, Nov 17, 2019, 8:47 PM
what a pr0 blog
by mathleticguyyy, Nov 9, 2019, 12:19 AM
$[asy]size(500); draw(polygon(7));[/asy]$
by FadingMoonlight, Jul 31, 2019, 11:11 AM
kala para na
by spy., May 4, 2018, 1:39 PM
So you've discovered this blog too? @archimedes15
by GeronimoStilton, Apr 5, 2018, 1:25 PM
What a dead blog...
by Archimedes15, Feb 19, 2018, 11:57 PM
bad physics. Relearn. Now.
by james4l, Aug 24, 2008, 7:15 PM
I already did.

With the new quote-simulation program (read my post on james4l's blog) I can slow my computer so much time goes backwards!

Just enter it for a thread with 1 trillion posts.

Time will flow baackwards.

Only 19.99! A 5000000 dollar value!

You can go backwards in time

Unfortunately, you'll have to stay there, because you can't go forward.
by pythag011, Aug 24, 2008, 1:32 AM
Nope it's 227 now. I should create some kind of anti-F5 button, so I can DROP a blog's views
by zephyredx, Aug 23, 2008, 6:33 PM
Whoever comes to this blog next will turn 225 views into 226
by pythag011, Aug 23, 2008, 3:34 AM
a.k.a. Mr. Ghost.
by zephyredx, Aug 22, 2008, 7:08 PM
BTW, if you go to microsoft word, double click n Mr.Green, and set brightness to 80% You get ghost Mr.Green.
by pythag011, Aug 20, 2008, 8:24 PM
Actually the beaver function is real...
by zephyredx, Aug 20, 2008, 2:24 AM
:D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D :D

SPAM!!!!!!!!!!!!!!
by pythag011, Aug 18, 2008, 5:24 PM
#1: 0 pts
comments: You have trivialized the problem by stating a direct reference to the solution of the problem.

#2: 0 pts
comments: irrelevant special case.

#3: 3 pts
comments: incoherent proof though the graders do applaud your use of a non-existent function

#4: 1 pts
comments: seriously, the joke's less funny second time through.

#5: 0 pts
comments: trivialization, not objectively stated the view of the contestant.

50% penalty for solving out of the time limit.

Your score is...

2 pts out of a possible 2000 pts
by james4l, Aug 18, 2008, 5:47 AM
LOL at your #2...
by zephyredx, Aug 18, 2008, 3:40 AM
1. By Perelman's proof, the Pionxare Conjecture is corect
2. No. The task of solving these problems has been proven to be NP, but not be P.
3. Apply an absolute zero Fourier Transform. Then, the velocity of every particle is 0. By the Fourier Untransforming Thereom, the velocity is f(R^3), where f is the Busy Beaver function (Zeb)
4. Yes. Consider the nth derivative of f(pi^e), where f is the busy beaver function. It must be an integer if pi^e is rational. But, it is positive and less than 1. Therefore, pi^e is irrational. Using the transcendality-irrationality bridge thereom, pi^e is transcendental.
5. This is a direct consequence of Zeb's conjecture.

How did you get into my blog?
by pythag011, Aug 18, 2008, 1:37 AM
IMO 2593 Problems:

Day 1:

You have 15 minutes.

#1 Prove the Poincare Conjecture.
#2 Is P=NP?
#3 Determine the velocity of every particle in Earth.
#4 Is pi*e a transcendental?
#5 Objectively show that the continuum hypothesis is true or false. Justify your response.
by james4l, Aug 18, 2008, 12:55 AM
Read the problem I just posted.
by pythag011, Aug 17, 2008, 12:38 AM
Peanut butter
by zephyredx, Aug 16, 2008, 10:53 PM

248 shouts

Random Trivial Problems

The thereom of mean similiarty.

by pythag011, Sep 17, 2008, 12:46 AM

4 Comments