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[solbjerg]

Hi all

A little "Triangle tipping" geometry problem

Attached

Cheers

solbjerg

Triangle tipping.zip

[demitris]

hi solbjerg

 

i calculated in a hurry appox. 219.8 cm

since 3 rounds are needed to reposition and in everyone travels 420 deg. arc

so distance=(3*420*2*3.14*10)/360= 219.8 cm

regards

[solbjerg]

Hi demitris

You were a little too quick :-)

First round 420°

Second round 450°

Third round 330°

Same result if you go the other way - just reversed.

Which makes the distance travelled by A = 209,44 cm

Phi by the way 355/113 is a close approximation → 3.141592

Cheers

solbjerg

° = Alt+0176

 

 

hi solbjerg

 

i calculated in a hurry appox. 219.8 cm

since 3 rounds are needed to reposition and in everyone travels 420 deg. arc

so distance=(3*420*2*3.14*10)/360= 219.8 cm

regards

[demitris]

hi solbjerg

 

thanks for the correction

 

cheers

[solbjerg]

triangle counting

 

Hi demitris

Have you seen those tests where you have to find how many triangles you can find inside a larger triangle?

The formular for this is

(n*(n+2)*(2*n+1)/8 )

Where n is the number of small triangles that make up the side of the larger triangle

When the number of small triangles is uneven you have round down to closest integer.

=INT(n*(n+2)*(2*n+1)/8 ) if you use Excel e.g.

Cheers

solbjerg

p.s. In 1969 I had a girlfriend that worked for an Insurance company. She attended a course arranged by the company. In order to create some togetherness/chumminess/hobnobbing they were presented with an equilateral triangle that had 4 small triangles to each side.And they then had to find out how many triangles they could find.

When she showed me that - we started to experiment with those with the sides 1-2-3-4-5 and wrote the results down in a list, after a while we could see a system in the results and then came up with this formular.

In future chumming sessions of this kind she could "sabotage" the hobnobbing. :-)

 

 

hi solbjerg

 

thanks for the correction

 

cheers

[demitris]

hi solbjerg

 

i didn't see that before

very difficult program it has to deals with math-Series(sequencies)

 

by the way a CYPRUS football team APOEL is coming to Copenhagen for a European Champions League match vs Copenhagen

 

cheers

[solbjerg]

Hi demitris

I am not sure I explained it sufficiently, so I add a picture of such a triangle.

An easy example where it is easy to count the 4 small triangles and the 1 large one - in all 5

(n*(n+2)*(2*n+1)/8 )

(2*(2+2)*(2*2+1)/8 ) = 8*5/8 = 5

Cheers

solbjerg

p.s. with the side 3

(3*(3+2)*(2*3+1)/8 ) = 15*7/8 = 13.125 → 13

with the side 4

(4*(4+2)*(2*4+1)/8 ) = 24*9/8 = 27

http://forums.iobit.com/attachment.php?attachmentid=1376&d=1250322657

 

hi solbjerg

 

i didn't see that before

very difficult program it has to deals with math-Series(sequencies)

 

by the way a CYPRUS football team APOEL is coming to Copenhagen for a European Champions League match vs Copenhagen

 

cheers

[demitris]

hi solb

 

it is easily understood

 

when i say is a very difficalt problem i refer to the finding of the math FORMULA

 

cheers

[solbjerg]

Hi demitris

Yes we had a very interesting evening counting all those triangles :-)

Cheers

solbjerg

 

 

hi solb

 

it is easily understood

 

when i say is a very difficalt problem i refer to the finding of the math FORMULA

 

cheers