plotting 7 points on a surface so that

Hi, sorry if I can't explain you the question properly. We need to plot 7 point on a surface so that: after picking any 3 point, the distance between at least two points should be exactly 1 unit

for e.g I thought hexagon and a point in the center. But it does not be true for every 3 points. I can't find solution more than 6 points

Note by Emre Tuzcu
2 weeks, 6 days ago

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You can see this works in every case except, when we choose A,D and G. Now if we rotate the right side in this way AG=1\overline{AG}=1 then we solved the problem:

Páll Márton - 2 weeks, 3 days ago

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Actually this looks logical but is it true for BFG

Emre TUZCU - 2 weeks, 3 days ago

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Its totally correct answer

Sahar Bano - 2 weeks, 3 days ago

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@Sahar Bano Right fool me :)

Emre TUZCU - 2 weeks, 3 days ago

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What does BFG mean? I found only Big F***ing Gun

Páll Márton - 2 weeks, 3 days ago

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@Páll Márton That was right. I thought wrong for a sec

Emre TUZCU - 2 weeks, 3 days ago

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1\leq1 or exactly one unit?

Páll Márton - 2 weeks, 5 days ago

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Exactly one unit. Also I think there may not be a solution

Emre TUZCU - 2 weeks, 5 days ago

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If exactly one this is impossible. If you draw an equilateral triangle and write the circles with radius=1, than there won't be engraving of the three lones in one point, so the number of points should be less than 4

Páll Márton - 2 weeks, 5 days ago

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Maybe in higher dimensions

Páll Márton - 2 weeks, 5 days ago

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Thanks for reply. Can you explain your proof withmore details. I didn't get it It may be impossible for 7 points but not for 5 or 6 points. If you draw a hexagon, it satisfies the conditions. I think it's impossible for >=7 points

Emre TUZCU - 2 weeks, 5 days ago

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If the task says that the distance between all of the points should be 1 unit, then the biggest number of points is 3. Only the mentioned triangle can satisfy the conditions. But if the task says that we can choose two from the three points, then the hexagon won't work. If the name of the hexagon is ABCDEF, than the distance between A, C and E isn't one unit.

Páll Márton - 2 weeks, 5 days ago

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@Páll Márton That's right but its true for square or pentagon

Emre TUZCU - 2 weeks, 5 days ago

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@Emre Tuzcu Yeah. Here is an interesting problem: Given 2006 points. In every case when we choose 3 points, then the area of the triangle with the selected points won't be bigger than 1 unit. Prove that we can cover these points with a triangle with 4 units area!

Páll Márton - 2 weeks, 5 days ago

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@Páll Márton From XV. NNMV 9. class.

Páll Márton - 2 weeks, 5 days ago

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@Páll Márton okay but actually this is totally different question

Emre TUZCU - 2 weeks, 5 days ago

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@Páll Márton anyway, thanks for you attention

Emre TUZCU - 2 weeks, 5 days ago

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@Emre Tuzcu You are wolcome!

Páll Márton - 2 weeks, 5 days ago

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@Páll Márton *welcome

Páll Márton - 2 weeks, 5 days ago

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@Páll Márton I have a figure with 6 points which satisfies the condition mentioned in the notes. I can share it if you want

Sahar Bano - 2 weeks, 4 days ago

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@Sahar Bano I doubt it

Páll Márton - 2 weeks, 4 days ago

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@Sahar Bano Share with us please

Páll Márton - 2 weeks, 4 days ago

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@Páll Márton

In the above diagram ACDEACDE is a square with side of one unit length. ABC\triangle ABC and FED\triangle FED are equilateral.

Now in parallelogram ABFEABFE, FB\overline{FB} is also of 1 unit length.

Sahar Bano - 2 weeks, 3 days ago

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@Emre TUZCU?

Páll Márton - 2 weeks, 3 days ago

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I tried to show it with dots on the keyboard but the blanks does not count here. If you think 2 equilateral triangle touching each other at the bottom (one's right bottom corner touches the others left bottom corner) This makes 5 point and 2 on the upside and 3 on the bottom, so draw last point to make 2 upside down triangle on the upside

Emre TUZCU - 2 weeks, 3 days ago

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I don't understand what does it mean :( The maximum number of dots is 5.

Páll Márton - 2 weeks, 3 days ago

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I edited it to the question

Emre TUZCU - 2 weeks, 3 days ago

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Nice work! I will write a c++ program when I have time.

Páll Márton - 2 weeks, 3 days ago

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I solved it with 7 points

Páll Márton - 2 weeks, 3 days ago

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Maybe incorrect, but I'm testing it yet

Páll Márton - 2 weeks, 3 days ago

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Thank you so much for your attention, now I can sleep in peace :) @Pàll Màrton and @Sahar Bano

Emre TUZCU - 2 weeks, 3 days ago

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You posted it 3 days ago :)

Páll Márton - 2 weeks, 3 days ago

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it was rough time :)

Emre TUZCU - 2 weeks, 3 days ago

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@Emre Tuzcu No! The rough time, when you must eat the food at school.

Páll Márton - 2 weeks, 3 days ago

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@Páll Márton Ahahah Actually I eat at the college no problem every time I go to school. Why its bothering you

Emre TUZCU - 2 weeks, 3 days ago

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@Emre Tuzcu The school has no money. That's something it looks like:

Páll Márton - 2 weeks, 3 days ago

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@Páll Márton oh, dude. I get it now. We usually eat better than this

Emre TUZCU - 2 weeks, 3 days ago

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@Páll Márton also, enjoy your meal. If you can :)

Emre TUZCU - 2 weeks, 3 days ago

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