[plainglazed]

You have at your "disposal" four of those fancy new-fangled compasses and an ultra-modern straight edge and a piece of ordinary bright white twenty gr/m

2

bonded letter-size paper. The compasses, being the latest and greatest, draw perfect arcs with both point and pen remaining perpendicular to the drafting surface and the pen drawing with the finest imaginable line weight. They are also infinitely adjustable to the nth degree. Of course the one downside to being so new is that once an arc is struck, the adjustment mechanism is permanently frozen. Now the straight edge is also of the most modern material and is straight on an atomic level; that is until you attempt to draw a twelfth line, at which point some bizarre reaction with the compass' ink or the space age alloy of the metal point irreparabably warps the patented polymer used, rendering it useless (research is now fully funded and ongoing to determine if it's the ink or the metal).

The objective of this challenge is to draw a perfectly regular five pointed star using only what's contained in your body and in the above discription.

[Guest]

I think the key thing to do would be to find the end points of a perfect regular pentagram on a circle. The rest would be to combine the relevant vertices to make the star which would need 5 lines.

now then, how can I locate the vertices of a pentagram on a circle??

Getting 5 points placed 72 degrees apart.. Hmmm

[Guest]

You have at your "disposal" four of those fancy new-fangled compasses and an ultra-modern straight edge and a piece of ordinary bright white twenty gr/m

2

bonded letter-size paper. The compasses, being the latest and greatest, draw perfect arcs with both point and pen remaining perpendicular to the drafting surface and the pen drawing with the finest imaginable line weight. They are also infinitely adjustable to the nth degree. Of course the one downside to being so new is that once an arc is struck, the adjustment mechanism is permanently frozen. Now the straight edge is also of the most modern material and is straight on an atomic level; that is until you attempt to draw a twelfth line, at which point some bizarre reaction with the compass' ink or the space age alloy of the metal point irreparabably warps the patented polymer used, rendering it useless (research is now fully funded and ongoing to determine if it's the ink or the metal).

The objective of this challenge is to draw a perfectly regular five pointed star using only what's contained in your body and in the above discription.

golden ratio. but it may use too many compasses

[Guest]

golden ratio. but it may use too many compasses

Yeah, I can get it with aforementioned technique using 4 compasses and 8 lines (leaving three spare lines to hold me over until the research on that straight edge is completed). Hard to show method, but can post later.

[plainglazed]

I think the key thing to do would be to find the end points of a perfect regular pentagram on a circle. The rest would be to combine the relevant vertices to make the star which would need 5 lines.

now then, how can I locate the vertices of a pentagram on a circle??

Getting 5 points placed 72 degrees apart.. Hmmm

right so far, at least by my method.

Yeah, I can get it with aforementioned technique using 4 compasses and 8 lines (leaving three spare lines to hold me over until the research on that straight edge is completed). Hard to show method, but can post later.

This I am excited to see. Now you've got me trying to solve my own puzzle. I have gotten it down to ten lines.

[Guest]

Yeah, I can get it with aforementioned technique using 4 compasses and 8 lines (leaving three spare lines to hold me over until the research on that straight edge is completed). Hard to show method, but can post later.

I must give credit to

http://www.geocities.com/robinhuiscool/Goldenratio.html for how to obtain the ratio.

Referring to my awesome paint drawing:

1. Draw line 1

2. Select a point A and use compass 1 of length x to measure twice x on line 1 to one side and label this point B. Using point A again, measure length x on the other side (x can be any lenth, but we'll assume you picked something small enough to fit 3x on line 1)

3. Construct a perpendicular line at point A using the points on line 1 which are x distance away and compass 2 of lenth y (again arbitrary)

4. Using compass 1 measure up from point A length x and label this point C.

5. Connect points B and C with line 3.

6. Using compass 1 measure out on line 3 from point C and label this point D.

7. Using compass 3 measure B to D and also mark this distance on line 1 from B and label it E.

8. Using compass 4 measure A to E. The golden ratio should be BE to EA.

Only compasses 3 and 4 are needed to construct the points of the star. Then connect the dots with 5 more lines to total 8.

[plainglazed]

Well done ljb. Much better than mine.

Draw a circle with center point O with the first compass.

Draw first line through point O and label the points of intersection with the circle A and B.

Draw arcs from point A and point B with the first compass intersecting the circle at points C and D (angles AOC, COD, and DOB all equal 60

o

).

Draw second line CD.

Draw arbitrary third line through point D.

Draw five successive arcs along this third line with compass two labeled D

1

- D

5

.

Draw fourth line from D

5

to C.

Draw an arc with the third compass from D

4

tangent to line D

5

C.

Draw another arc with the third compass from some point F on D

5

C.

Draw fifth line from D

4

and tangent to the arc drawn from F (at E

1

above) and extended to where it intersects line CD at point G.

Draw sixth line from O through G to point of intersection with the circle at point H (angle COH = 1/5 of angle COD or 12

o

making angle AOH = 72

o

).

Draw an arc with the fourth compass from point H to point A.

Draw three more successive arcs with the fourth compass from A to where it intersects the circle at I, J, and K.

Draw lines seven through eleven from AJ, JH, HI, IK, KA to form the star.

I suspect DeeGee may have had this solution all along judging by his first post and the fact that I got the idea for this puzzle from his truly inciteful solution to Jerbil's last very cleverly conceived geometric construction.

[Guest]

I suspect DeeGee may have had this solution all along judging by his first post and the fact that I got the idea for this puzzle from his truly inciteful solution to Jerbil's last very cleverly conceived geometric construction.

Well, thank you for being so generous. Actually, I never had all the details in mind... Thought a bit about how to get points 72^o apart on the circle but never got that far!!

[Guest]

Well done ljb. Much better than mine.

Draw a circle with center point O with the first compass.

Draw first line through point O and label the points of intersection with the circle A and B.

Draw arcs from point A and point B with the first compass intersecting the circle at points C and D (angles AOC, COD, and DOB all equal 60

o

).

Draw second line CD.

Draw arbitrary third line through point D.

Draw five successive arcs along this third line with compass two labeled D

1

- D

5

.

Draw fourth line from D

5

to C.

Draw an arc with the third compass from D

4

tangent to line D

5

C.

Draw another arc with the third compass from some point F on D

5

C.

Draw fifth line from D

4

and tangent to the arc drawn from F (at E

1

above) and extended to where it intersects line CD at point G.

Draw sixth line from O through G to point of intersection with the circle at point H (angle COH = 1/5 of angle COD or 12

o

making angle AOH = 72

o

).

Draw an arc with the fourth compass from point H to point A.

Draw three more successive arcs with the fourth compass from A to where it intersects the circle at I, J, and K.

Draw lines seven through eleven from AJ, JH, HI, IK, KA to form the star.

I suspect DeeGee may have had this solution all along judging by his first post and the fact that I got the idea for this puzzle from his truly inciteful solution to Jerbil's last very cleverly conceived geometric construction.

plainglazed - I don't think your angle disection is valid. It looks close but is not accurate. If it were as easy as disecting a line, then the trisection of an angle would not still be one of the "impossible" geometric constructions. If you think otherwise, I would be interested to see a proof.

[Guest]

plainglazed - I don't think your angle disection is valid. It looks close but is not accurate. If it were as easy as disecting a line, then the trisection of an angle would not still be one of the "impossible" geometric constructions. If you think otherwise, I would be interested to see a proof.

I think it is valid if you are referring to the trisection of angle AOB (180^o). Here's why:

Consider triangle OBD

OB = OD = BD (all are equal to radius of the circle) and similarly in triangle OAC,

OA = OC = AC

So, both the angles AOC and BOD are 60^o meaning that angle COD is also 60^o

[plainglazed]

ljb must be referring to sectioning segment CD into fifths and the corresponding angles thru the centerpoint of the square not equalling 12^o. I can prove that they're not so guess I wont be proving that they are (yelping with tail between legs back to Words). Sorry all.