Hi Brian
-- My nodeeditor has the wrong node, infos>Display

I'm not sure which version I'm using. Maybe mine is the one that is outdated.
The "Display" node initially was inside "r2d3" menu.

-- Also, I do not have the "Blue/Green/Teal" nodes

These nodes are "output" nodes that I changed their colors and used as label. (right click on the node >> "colors")
Also, you can double click on the canvas. This way the node's name and address will be displayed in the properties panel.

Hi, Mip...

But part of the quiz is all of the vertices MUST be in a circle circumference...



So, from the screenshot, if you pick any 3 of the 5 vertices as references for a 3 point circle in Moi, then ALL of them should be exactly on this circle circumference.

Hi, Brian...

That looks very sophisticated for me. ^_^;
I really wish that I'm as smart as you in math.

Thanks for the help and effort.

Cheers!

Thank you MO.

- Brian

Hi Elang

Congratulations on solving the puzzle!
Your numbers and angles look about as good as they can be, given 7 decimals of precision, at X = 10.


After carefully redrawing as X = 10, with radius of 9.2819138, these are some values realized:
Radius = 9.2819138 (This value might be slightly too great, in decimal 7.
Angle A = 97.781889
Angle B = 114.812072
Angle C = 114.812074 (Slightly different)

These numbers are nearly the same as your numbers, +/-.

Construction can use a variety of MoI commands.
Zooming in a huge amount, shows very slight anomalies

I do not know if X = 100 would make much difference. Maybe pick up an extra decimal.

- Brian

Hi Brian

Thank you for kind words. I've got lots reference from all posts here which led me to solving the problem which I appreciate very much. Now if only the process I've been through can be automated, it would be very nice. Perhaps via some script?

And yes, zooming in huge amount will show anomalies, but I guess this is natural since the precision is not infinite in every ways possible.

Cheers!

Hello Elang,

I wonder how I missed your post! As I love geometric puzzles!

I think by now you have solved your puzzle, However I would like to examine a possible solution myself, so, please answer the following questions:

> So we provided with 3 lines:
> - 1 horizontal blue line with length of X√2
> - 2 magenta lines with length of X

> The task is to arrange them in specific ways so that: they form a continuous polylines with each endpoints are exactly on a perfect circle circumverence (red circle), like in the provided illustration (it's actually not an acurate drawing I
> made in Moi). The real task is to form a pentagon with 4 magenta lines (length = x) and 1 blue lines (length = x√2), but I believe we can ignore the other 2 since they'll be added later by mirroring the 2 existing magenta lines horizontaly.

1- the pentagon should be regular or it could be irregular? (I know if the blue line is going to be the base of the pentagon then we are talking about irregular pentagon I also know u have mentioned it! however, I need to be sure.)
2- Tell me if we are provided by all the mentioned lines. (or should we make a line from other line? for example blue from red?)
3- Tell me about the initial position of the 3 lines!

- Psygorn

I think that the desire was that TWO of Four X length lines (chords-to-be), are to be placed or moved, perhaps by Rotation, until some snap is achieved, (perhaps at apex).

The trouble is that as the base angle changes, the other 3 angles change, and there seems to be no way to achieve a Snap solution.
(The other 3 angles are equal to each other.)

The angle at B is a function of the base angle at A2, so as the (chord) rotation occurs at A2, if there was some way to Constrain the angle at B, by said formula, a snap to the top center of an increasing 3pt circle might be possible. (???). History of 3 point circle does not seem to occur for movement of the 3rd point in its creation AFAIK.

Constraint of 3 angles to be equal, based upon change in degrees of a 4th (base) angle does not seem to be available in MoI(?)

- Brian

Another factor is that the value of the solution radius turns out to (seems to) have more than 12 decimal digits, so perfection may not be possible, given floating point limitations.
So a solution within a small epsilon is acceptable, IMHO.

The 4 chords can be on the circle, but have slightly different lengths,
or the chords can be of equal length, but two of the vertices be slightly outside of, or inside of, the circle...IMHO
And/or slightly different angles...

Not yet all read above but here my solution as usual very rustic brute force by "hand" but...i obtain the solution! :)
Circle by 3 points and big zoom for draw some tests :) Maybe 20! :)
AB = hypothenuse of a rectangle triangle 1*1 * hypo

I found the solution with 0.1234567 decimals permitted by Moi!

Radius found of the red Circle : 0,9281914 (max definition)
Here x = 1
Five points of the pentagon will be on the circle!

Of course when you have this first solution any resize will give you the other infinite solutions! :)

After the third C point i ask the length of the segment... if not 1 i draw another one C ! (up or down following results) :)





https://moiscript.weebly.com/uploads/3/9/3/8/3938813/longueur1.3dm

Ps seems there is something ultra simple that i have seen in writing this! :)

Intolerable suspense! :) I must verified my intuition!

Hi MO (MO_TE),

When I load "pentagon_Quiz.nod" the nodeditor's run button looks deactive (meaning it does nothing)! What could be the reason? How can I fix it?

- Psygorn

Hi, Psygorn... sorry for late reply.

1. Yes... it would be an irregular pentagon with: 1 edge length = X√2 while the other 4 edges length = X
2. The necessary elements is all mentioned already.
3. Actually, there is no specific initial position for the lines except it would form an irregular pentagon like mentioned in point 1, AND if we draw a 3 point circle through 3 vertices of the pentagon then ALL vertices should by on the circle circumference.

Cheers!

Hi Pilou,

That's very much similar of how I solved the problem.

:)

yes very "physcical" it's the less headaches! :)
Only result is counting!
I will continue to find something very simple! ...

Hi psygorn
Sorry about that.
I guess it has to do with the "display" nodes I used. ("NE" old version).
Wrong nodes have a red box on their upper left corner.
You can delete them or replace them with similar nodes.

Also I tried to make a more accurate pentagon. " pentagon_Quiz_Loop_Method.nod "
This time I used "loop" nodes. Give it a few seconds to see the pentagon !

So close! :)

Hi Elang,

I know as of now you have already solved the problem.

However, I think I might be able to correct your calculations a bit further.



Though I think it is a difficult problem for your nephew. But if he has more of these puzzles I would be happy to see them :-)

Remember alpha can have different values I chose the value that helps solving the problem.

The numerical method was done using a pocket calculator. So, maybe there are methods to calculate it with even more accuracy.

Do not take the last digit as granted. and for two alphas I think you can assume it is equal to 114.8120745 degrees.

If u use this amount then Angles A,B & E would all be equal to 114.8120745. However, even in this situation when u superzoom into it there u can see the corners are not on the big circle (which I think is not a calculating issue, it is rather displaying issue which I personally believe u can safely ignore it.)

And I failed to find a simple genius method to solve this problem, maybe there isn't such a solution. However, I cannot be sure!

- Psygorn

Hi Psygorn.

Thank you very much for the explanation. To be honest, I can only follow the first two lines from your picture. ^_^
However I've shared the picture to my nephew which amaze him quite a lot.

The original quiz was in Bahasa Indonesia which translation sounds like this:
"There are 3 lines. One line has length x√2 while the other has length x. Arrange the three of them into half pentagons so that all the ends are exactly on the circumference of a circle. Show me the picture. For bonus point: Mention the size of each corner formed and the radius of the intended circle."

The students has to solve this in their preference CAD application.

<<The students has to solve this in their preference CAD application.

So it's was a geometric solution asked and not a mathematical one! ;)

And it's really meant to be solved using constrains if we want to avoid calculations :
Here is a way to solve it using Freecad :

HI Pilou,

Indeed it is... Please forgive my English for misconceptions.

No problem! :) English is not my cup of tea too! :)