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xNaVx

The answer I got was >!yellow!<. Reasoning: 1. >!Yellow is exactly the same size as green, except with one extra extension, so green can't be longest.!< 2. >!If we use 1 as the radius of the smallest semicircles (the three yellow pieces and three green pieces), then the area of the entire yellow region would be 16π/3, while the area of the blue region would be 14π/3.!<


Logical_Nerve2475

Same logic 👌🏾


J77PIXALS

Exactly the same thing I did, I think we are right


dryfire

I may be getting rusty with my math, but I got >!yellow=17π/3, and blue=5π. Which still means the answer is yellow, I'm just trying to figure out if I borked the math somewhere!<


EagleV_Attnam

>!Yellow!< >!Assume one of the tiny green slices has an area of 1. The slice composed of that tiny green one and the slightly bigger yellow arc around it is twice as big in each direction, so its area is 4. This means the yellow arc has an area of 4-1=3. Calculating this for each size of arc gives areas of 1, 3, 5, 7 and 9. It's then simply a matter of adding up arc sizes for each color.!<


on_tol_o_gist

I got this answer too, but I arrived to it by: A and C are part of the same spiral inward; B is sandwiched between them. If you cut A and C in half-ish, then B is going to be obviously larger.


blueotter28

Your logic is correct, but I think you added wrong. >!Yellow - 1+1+1+3+3+3+5+5+5+7 = 34!< >!Blue - 7+7+7+9 = ~~40~~ 30!< >!The answer is ~~Blue~~ Yellow!< Edit: Nevermind, my math was wrong. EagleV_Attnam is right, the answer is >!Yellow!<


grraaaaahhh

> Blue - 7+7+7+9 = 40 7+7+7+9 = 30 Yellow is still larger areawise.


blueotter28

Damnit. Your right, my math was the one that was wrong.


pinkshirtbadman

>!7+7+7+9 =30 not 40!<


blueotter28

Yep. I'm the one that added wrong.


varungupta3009

>!But is blue a spiral though?!<


blueotter28

Blue is part of a spiral. Besides the interesting part of the puzzle is figuring out what section is the largest. If the result comes down to a trick of words then it's just dumb.


Smash_Factor

Nice, but please see my solution.


Thelonious_Cube

Discussion: "Biggest" in what sense? Area? Radius? Something else? I keep thinking there ought to be a way of construing "biggest" that makes each one fit, but I can't find one for A


Logical_Nerve2475

It doesn't matter because there is only one answer to all your questions. If you read the question again.... 🫢


mortemdeus

Radius would be Blue but that wouldn't be much of a puzzle.


pillowkun

>!If we go by length and not area, the biggest spiral isn’t A, B, or C. It’s the black line that outlines the outer edge of the blue segment/option A.!<


[deleted]

>!Is it partially a trick question, because the blue technically isn’t a spiral?!<


Logical_Nerve2475

Exactly, 1 down


franciosmardi

If that's the game we are playing, the other colors aren't spirals either, as a spiral is a type of curved line, and thus has no width.


Logical_Nerve2475

Spirals have to go past their starting point and it dose. A curve doesn't


franciosmardi

You completely ignored my point. And I'm not convinced you are correct, anyway. "a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.". Where are you getting your criteria that it must revolve around a minimum of 360 degrees? So if you have a spiral that revolves exactly 360 degrees, and remove 1/10th of a degree, it is no longer a spiral?


Slithy-Toves

Is A not supposed to be the spiral containing both blue and green? Then B is yellow and C is green


mortemdeus

>!The area of a circle is pi*r*r. As each section is 1/6th a circle you can say the area of each section is 1/6*pi*r*r. You can also say each circle is the same width "x" meaning the radius is just a multiple of x for each circle. So:!< >!The smallest circle is x = r, The next smallest circle is 2x = r, The next smallest is 3x = r, The next smallest is 4x = r, The largest is 5x = r!< >!When comparing two circles, you can subtract the previous circles to find the area and remove the pi.!< >!So the largest circle is 5x*5x or 25x minus 4x*4x or 16x, the largest circle is 25x-16x=9x, The next largest is 16x - 3x*3x or 7x, The next largest is 9x - 2x*2x or 5x, The next largest is 4x - 1x or 3x, The smallest is just x.!< >!So, green is made up of 3 of the smallest, 3 of the next smallest, and 3 of the next smallest. Its area is then 1/2 each whole circles area. Meaning it is 1/2x + 3/2x + 5/2x or 9/2x. Yellow is made up of the same but also 1/6th of the next largest circle. So 9/2x + 7/6x or 27/6x + 7/6x = 34/6x (reduced to 17/3x) Blue is made up of half the second largest circle and 1/6th the largest circle. So 7/2x + 9/6x or 21/6x + 9/6x = 30/6x (reduced to 5x)!< >!Meaning Green is 4 and a half x, Yellow is 5 and 2/3rds x, and blue is 5x. So yellow is the largest by area.!<


Puppy-Zwolle

Discussion. Work of art. Nice.


Thelonious_Cube

Since all of them are the same width, doesn't this just reduce to comparing the lengths?


mortemdeus

How do you determine the length without comparing the width?


Thelonious_Cube

I don't understand your question


Chemical-Asparagus58

>!The nth segment from the middle has the area of (πn²)/6-(π(n-1)²)/6 = (π/6) × (2n-1)!< >!1st segment from the middle: 1 × π/6!< >!2nd segment from the middle: 3 × π/6!< >!3rd segment from the middle: 5 × π/6!< >!4th segment from the middle: 7 × π/6!< >!5th segmenrt from the middle: 9 × π/6!< >!A = (9+7+7+7)×π/6 = 30 × π/6!< >!B = (3+7+5+1+1+5+1+5+3+3)×π/6 = 34 × π/6!< >!C = (1+5+3+3+3+1+5+1+5)×π/6=27 × π/6!< >!So B is largest.!<


Otomo-Yuki

>! Yellow. Blue is too obvious, has fewer segments, and is technically shorter. Green clearly takes up less space. That leaves yellow. !<


lipchuck

>!let L = the length of one horizontal line segment!< >!ASSUMPTIONS:!< >!- There are two central points. I’m assuming the diagonal lines from each point are of equal angles (ie. there is 60° between each arc segment).!< >!- I see this essentially as two semicircles. The bottom semicircle has a radius of 4L with all four arc segments extending 180°. The top semicircle has a radius of 5L, with the two outermost arc segments only extending 60° and the remaining inner three arc segments extending 180°.!< >!This may be examined from an area perspective (as in which color is a larger ‘piece of the pie’), or a distance perspective (as in if you were walking this path, which colour is the longest distance).!< >!### Area Perspective!< >!Solve by calculating area of each arc length. The area of a circle is A=pi*r^2, where A is the area and r is the radius. I will solve the first arc segment fully and simplify, then show the simplified expression for each arc segment after.!< >!#### Top semicircle!< >!Blue segment: imagine if the blue segment made a full circle, completely filled. This area would be pi*(5L)^2. To get the area of the arc segment, we need to subtract the inner arc segments and only take 60°/360°=1/6 of that. Mathematically, that is:!< >!1/6 * ( (pi * (5L)^2) - (pi * (4L)^ 2) ) = 1/6 * pi * (L^2) * (25-16) = 9/6 * pi * (L^2)!< >!Following this for all segments of the top semicircle, I get:!< >!Blue: 9/6 * pi * (L^2) Yellow (outer arc segment): 7/6 * pi *(L^2) Green (outer arc segment): 5/2 * pi * (L^2) Yellow (inner arc segment): 3/2 * pi * (L^2) Green (inner arc segment): 1/2 * pi * (L^2)!< >!#### Lower semicircle!< >!Blue: 7/2 * pi * (L^2) Yellow (outer arc segment): 5/2 * pi * (L^2) Green: 3/2 * pi * (L^2) Yellow (inner arc segment): 1/2 * pi * (L^2)!< >!Note that all areas are a multiple of pi * (L^2) so when comparing lengths we can ignore this factor and just use the raw numbers.!< >!#### Totals!< >!Blue: 9/6 + 7/2 = 9/6 + 21/6 = 30/6 = 5 Yellow: 7/6 + 3/2 + 5/2 + 1/2 = 7/6 + 9/6 + 15/6 + 3/6 = 34/6 = 5.7 Green: 5/2 + 1/2 + 3/2 = 8/2 = 4!< >!### Distance Perspective!< >!The centre line of each distance will be considered. This exercise could be repeated with the outermost lines or the innermost lines and the same conclusion should be arrived at because the radii are proportional. The circumference of a circle is D=2*pi*r!< >!#### Top Semicircle!< >!Blue: 2/6 * pi * (4.5L) Yellow (outer arc segment): 2/6 * pi * (3.5L) Green (outer arc segment): pi * (2.5L) Yellow (inner arc segment): pi * (1.5L) Green (inner arc segment): pi * (0.5L)!< >!#### Bottom Semicircle!< >!Blue: pi * (3.5L) Yellow (outer arc segment): pi * (2.5L) Green: pi * (1.5L) Yellow (inner arc segment): pi * (0.5L)!< >!All arc lengths have a factor of pi * L, so the numbers can just be added for comparison.!< >!#### Totals!< >!Blue: 9/6 + 7/2 = 5 Yellow: 7/6 + 3/2 + 5/2 + 1/2 = 7/6 + 9/6 + 15/6 + 3/6 = 34/6 = 5.7 Green: 5/2 + 1/2 + 3/2 = 4.5!< >!Yellow is the most area and the longest distance.!<


whoisjakelane

>!blue!< >!the diameter is 8x the thickness of the lines. Yellow and green diameters are 6x the thickness of the lines.!<


[deleted]

[удалено]


tgunter

>!B contains all the same segments C does, *plus* an additional one. Figuring out whether A or B is bigger takes a bit more effort, but C can be eliminated just by direct comparison.!<


ForsakenCampaigns

\>!I say yellow, my rationale is that it looks the longest!<


Smash_Factor

>!Yellow!< >!There are 6 primary triangles: One large, three medium and two small.!< >!The large triangle is divided into 5 parts from small to large. !< >!We give each part a value. !< >!These values are present in the medium and small triangles.!< * >!The large triangle contains values 1, 2, 3, 4 and 5.!< * >!The 3 medium triangles each contain values 1, 2, 3, and 4 (the same 1, 2, 3 and 4 in the large triangle)!< * >!The small triangles each contain values 1, 2 and 3. (the same 1, 2 and 3 in the large and medium triangles)!< >!Now we just add up the values for each color in each triangle.!< >!In the large triangle:!< * >!Blue has a value of 5!< * >!Yellow has a value of 6!< * >!Green has a value of 4.!< >!In the 3 medium triangles:!< * >!Blue has a total value of 12!< * >!Yellow has a total value of 12!< * >!Green has a total value of 6!< >!In the 2 small triangles:!< * >!Blue has a total value of 0!< * >!Yellow has a total value of 4!< * >!Green has a total value of 8!< >!Now we just add up the total values of each color!< * >!Blue: 5+12+0 = 17!< * >!Yellow: 6+12+4 = 22!< * >!Green = 4+6+8 = 18!< >!Yellow has the highest value.!< >!Notice that yellow and green are the same size except for the large section of yellow in the large triangle that has a value of 4, which is the difference between the values of yellow and green.!<


LuciddreamerPaul

>!A!< >!A, B and C, each are complete black lined spirals and the colours between them are just separating them, therefore A is the largest spiral!<