[random7]

Let c be a fixed length, fixed in 2-dimensional space, which is the longest side of a triangle; let the other sides of this triangle be a and b, with variable lengths; let V be the vertex to the sides a and b; and let M be the midpoint of c.

By:

1. Colouring “the region mapped by the vertex V under the condition a²+b² > c²” the colour beige;
   
2. Colouring “the locus of the vertex V under the condition a²+b² = c²” the colour beau-blue;
   
3. Colouring “the region mapped by the vertex V under the condition a²+b² < c²” the colour blue (light);
   
4. Colouring “the region mapped by a point, which is within distance = c/8 of the point M” the colour black (note: if this region overlaps with another region, black is a more dominant colour); and
   
5. Colouring the leftover uncoloured regions the colour bistre;
   

What is the name given to the resulting mathematical picture?

(Remember to use spoilers to allow other problem-solvers to come to the answer in their own time)

[Guest]

Sounds like it will look like an eye.

[Guest]

The dotted line is the line of length "c"

The colors may not be the same as you wrote

Edited June 1, 2010 by DeeGee

[Guest]

The dotted line is the line of length "c"

The colors may not be the same as you wrote

That's good but what's the difference between the beige and brown colors outside the circle? I think they should all be beige...

[Guest]

From my sketches, it looks to me like he picture is of a human eye (blue). The black region is the pupil. am I right?

[superprismatic]

It seems to me that 1, 2, 3, and 4 colour the entire plane. There

doesn't seem to be anything left over to colour bistre.

I think the answer is ANNULUS.

[Guest]

BULLSEYE!

[random7]

Sounds like it will look like an eye.

Sounds like a guess? = P I like your projective ability though = D

The dotted line is the line of length "c"

The colors may not be the same as you wrote

Very very close! The beige region may need a re-think. I am very glad you put a lovely picture up = D

That's good but what's the difference between the beige and brown colors outside the circle? I think they should all be beige...

The key to DeeGee's reasoning lies within the introductory paragraph in the original post.

From my sketches, it looks to me like he picture is of a human eye (blue). The black region is the pupil. am I right?

Yes! Very well done = D If you have a scanner, I'd love to see your sketch. Did you notice any red-herrings in this puzzle?

It seems to me that 1, 2, 3, and 4 colour the entire plane. There

doesn't seem to be anything left over to colour bistre.

I think the answer is ANNULUS.

You might want to read the original post a bit more carefully; the answer "should" have closed regions for 1 to 4.

BULLSEYE!

lol

[Guest]

^ Ah, I see:

Let c be a fixed length, fixed in 2-dimensional space, which is the longest side of a triangle;

Details details...

I'll make a new sketch in Flash once I get back home this afternoon...

(though if anyone else wanna try, put two circles around each ends of vector c with radiuses of c's length and the area that combines the two circles is the answer to #1...)

Edited June 2, 2010 by Anza Power

[Guest]

i'd say a lunar eclipse especially coz of the specific colour code:

blue being the earh

the moon in the dark

and the sunlight in beige

PS: Dont get the reason for the 2 triangular parts

[Guest]

This is what i got:

The colors I looked up in Wikipedia and copied their hex codes from there

Edited June 2, 2010 by Anza Power

[Guest]

eye.bmp

Hey Anza, what colors did you use for the blues? I used the wikipedia colors too and mine look much lighter.

beau blue = (188, 212, 230) light blue = (173, 216, 230)

PS - Also, can someone please tell me how to post pictures? I added it as an attachment to this post, then added it to the post, but it doesn't show. GRRRR!

Edited June 2, 2010 by Drexlin

[random7]

I shall award this thread to these fine problem-solvers:

From my sketches, it looks to me like he picture is of a human eye (blue). The black region is the pupil. am I right?

This is what i got:

The colors I looked up in Wikipedia and copied their hex codes from there

In an attempt to insert a red-herring/Easter-egg into the puzzle, I have left one thing open to interpretation; the colour of the iris should have been read as "light-blue", but it can definitely be read as blue.

Here is my picture (which looks exactly like Anza Power's picture, except for the iris' shade of blue):

The SVG file can be downloaded here: http://www.mediafire.com/?yyzq2jmmyyz

Using a theorem for circle geometry, all triangles that have a right-angle opposite the side c lie on the circle to which c is a diameter of; thus, all of the vertex V that lie on this circle will form a triangle that satisfies Pythagoras' theorem, and thus #2 of the puzzle. Using the very-special triangle a+b = c, which has vertex V within this circle, it can be seen that c² = (a+b)² = a²+b²+2ab > a²+b², which is the condition in #3; this shows that #3 is the region inside this circle, and thus that #1 is outside this circle. For showing that #1 is the region outside the circle, we look at the equilateral triangle a = b = c, which has vertex V outside the circle; a²+b² = 2c² > c², which is the condition for #1. Now since c is the longest side to the triangle, the limit to the lengths of a and b is the length of c; thus the vertex V will always stay within the intersection of the two circles of radius c, and with centres about the endpoints of c. This gives the special region for #1, seen in the picture (the sclera). Thus, to finish off the picture, the region outside this intersection satisfies #5, and the region described in #4 is the circle of radius c/8, with centre about the point M. The final mathematical picture is the human eye.

Red-herrings/Easter-eggs:

• The final picture is what might seem to be an African with blue eyes. This is interesting since MOST Africans have brown eyes, since the blue-eye gene mutation originated in Europe.
  
• All the colours in the puzzle start with the letter "b". I can't think of a witty reason for doing this, but if someone thinks of one, post it, and everyone that tries this puzzle on their friends will have an extra special Easter-egg = )
  

I hope you enjoyed this puzzle, as much as I have enjoyed conjuring it = D

- random7

[Guest]

eye.bmp

Hey Anza, what colors did you use for the blues? I used the wikipedia colors too and mine look much lighter.

beau blue = (188, 212, 230) light blue = (173, 216, 230)

PS - Also, can someone please tell me how to post pictures? I added it as an attachment to this post, then added it to the post, but it doesn't show. GRRRR!

The colors I just looked up beige and baby blue, normal blue I picked out myself...

Also, for embedding pics, I think it's because your picture is in bmp, next time save it as JPEG/JPG, or if you're using windows Paint save it as PNG cause Paint sometimes messes JPG...

[Guest]

Thanks Anza! Worked like a charm!

BTW, to the OP... great puzzle! More like these please. I know they probably take a lot to prepare, but I really enjoyed this one.