Hi, Brian

Indeed it needs a constrain feature like i mentioned in the original post. But nephew only have Moi and love it so much that I won't 'spoil' him with other app which made we want to solve the quiz ONLY in Moi. Also, seems like you're much more smarter than me in math, so I can't understand much of your 'math talks' in your posts. But I appreciate much for the effort and please continue to do so if you please. :)

Cheers!

Hi BurrMan,

Yes it is... Only in the quiz, the red circle comes in the last order which make it tricky. ^_^

Hi All

I just found the video which very close to the quiz above, and how to solve it... only, it's done via Inventor using constraints like my friend sugested:

https://youtu.be/1xsWKAoXYk4?t=21

(it is in 0:21 through 1:08)

cheers!

Hi Elang,
""""""""
- The horizontal line of A1-A2, with x√2 length comes first in the quiz.""""""""""""

Here is a video I made creating a random x√2 value.



It works with any of the other 3 values given at any value.

The V axis is also irrelevant. All the rotation in the video is just to express it. The 3 point arc is valid. If you had geometry in some random world coords that you didnt want to move and rotate around, you could create a CPlane in that area on the Axis of your choice.

They use constraints in inventor because thats how inventor works!

Also, notice the 60x60x60 triangles the guy in inventor makes @1.08

He’s really just making random connection lines then telling them to be 60x60x60 triangles (his constraints)

But we want your nephew to understand trig

Also, he wants to do it in MoI! Its a simple solution with MoI’s toolset.

Here is another way to build a regular pentagon without using calculations or constraints.
While not the fastest way, it shows an easy method to get a 36 degree angle.
Hope you will find it interesting. Trig without inTrigue...

Radius of circumscribed circle of an irregular polygon

https://math.stackexchange.com/questions/2799954/finding-diameter-of-circumscribed-circle-of-an-irregular-polygon

Uses the Law of Cosines.

This can be used for the PentaChord puzzle.

m = number of sides with length A
n = number of sides with length B

The formula is:
m * arccos( 1 - ( A*A / 2*r*r ) + n * arccos( 1 - ( B*B / 2*r*r ) = 360 degrees.

For our puzzle, using length scale of x = 10:
m = 1
A = 10 * sqrt(2)
A*A = 100 * 2 = 200
n = 4
B = 10
B*B = 100

m * arccos( 1 - ( A*A / 2*r*r ) + n * arccos( 1 - ( B*B / 2*r*r ) = 360 degrees

arccos( 1 - ( 200 / 2*r*r ) + 4 * arccos( 1 - ( 100 / 2*r*r ) = 360 degrees

So the function to solve for is:
arccos( 1 - ( 100 / r*r ) + 4 * arccos( 1 - ( 50 / r*r ) - 360 degrees = 0

Radius "r" must be solved for. (with 40 year old calculator ? :-)

or solved with an Excel spreadsheet. (Somehow)

I think that the 360 is subtracted on the left side, setting the equation to 0?
Also see if the arccos is dealing with degrees or radians???

Increment "r" until some tolerance is achieved.
For scale x = 10, the approximate value of "r" is 9.2814, which is probably less that the actual value of "r".
(Some other values of approximate "r" are 9.2822, 9.2826.)
Might try an online calculator to test approximate "r" of 9.2814, to see if it is close to 0?

- Brian
With some learning I could probably do the Excel "macro".

https://en.wikipedia.org/wiki/Bisection_method
I suppose this could be done in Javascript?

Yes, this is breaking the "No Math" rule :-)

I used the computers calculator, manually with the formula, with test "r" = 9.2814, which resulted in 360.02368331... minus 360, which is close to zero.
Which is encouraging.

I have not yet tried to do a function solve...

- Brian

Actually, a quick Excel spreadsheet can replicate the Radius function equation, for a multitude of candidate radii. Maybe tomorrow.

- Brian

Hi
It's a very interesting and difficult quiz to solve inside moi. Looking at the math makes me dizzy. :)
I kinda solved it inside the nodeeditor by brute forcing the quiz conditions. (With 0.005% tolerance)
Take a look at attached file.

Hi MO,

My nodeeditor has the wrong node, infos>Display
Where is the latest Display node? I have Jame's Sept 14, 2020 nodeeditor version. Is it still the latest?

Also, I do not have the "Blue/Green/Teal" nodes which have one input, and have Title, Style, and Edges, where the Title serves as a label.
Where is a copy of this node located?

After replacing Display node, and removing the several "label" nodes, your script ran.
Your Radius shows as 0.9293, for Scale X = 1
The length of your 4 unit chords are different, and do not equal 1 unit.
zooming way in shows top and left points slightly outside of the circle.

-Thankyou
- Brian

Hi All,

I think I've solved it, though there are few very tiny errors...



So I made plenty-plenty trial n error by rotating the green circle (on the right) with A2 as its pivot. Every time I rotate this circle, I make a 3pt Circle (red) through A1,A2, and B, to check if this circle intersect all this circle, green circle, and vertical axis in exactly one point... The goal is to make this red circle touch all of A1, A2, B, and C where C must be on the Vertical Axis. It's very impractical but does the job, I guess..

As you can see, there is very tiny difference at the red circle radius where the vertical radius has a 0.0000001 deviation from the other. Also, the angle of C and B differs about 0.0000011 deg. I think this is good enough (?)

I'm still looking forward for much simpler and better solution, though... so please write anything should you feel necessary.

Cheers!

Here is another one. It respects the 2 statements "x" and "x * square root(2)".
The key is to circumscribe the pentagon instead of inscribe it.
With circumscribing, it is possible to use Tangent snapping.
Mirror History and rotation to tangency are essential to "fit" the sides.

I dd an Excel spreadsheet to calculate the Radius, semi-manually.

A scale of X = 10 was used.
MoI seems to allow a setting of 7 decimal places.
Note: A scale of 1000 with 7 decimals does not seem to work well in MoI, as far as snaps and intersection went. (?)

At X=10, the best Radius, limited to 7 decimals, was 9.2819138 units
In Excel, the error was -1.61E-8

A more precise Radius, with 13 decimals, was 9.2819137798526, with error of 2.50733E-12, BUT I think that this value is unusable in MoI (?)

At X=100, the best Radius, limited to 7 decimals, was 92.8191378, with error of -1.16072E-10.

So there is not a "Perfect" solution, with the number of decimal that can be used. The radius value might be transcendental.

The Excel formula in cell B29, which references the variable values, for Radius cell A29, is:
=$B$22*ACOS(1 - $C$23*$C$23/(2*A29*A29))+$B$24*ACOS(1-$C$25*$C$25/(2*A29*A29))-(2*PI())

The Excel spreadsheet is attached, and with a little practice, anyone can build one. Spelling error, radans should be radians. (ACOS() uses radians not degrees of angle.
I learned the rudiments of Excel many years ago.

- Brian

So the puzzle can be built in MoI, using the "best" radius of 7 decimals, at X = 10, or X = 100.

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!