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# how to find the coordinates of the corner of a star

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how to find the coordinates of the corner of a star

Guest May 28, 2015

#2
+80866
+10

I'm assuming the "star" can be fashioned out of a pentagon inscribed in a circle having a radius of 1.  And the center of this circle is located at (0, 0).

I'm also assuming that the "top" corner (vertex) of the star is located at (0,1)

Then.......proceeding clockwise, the next corner (vertex)  is located at (cos (18), sin (18))  = about (.951, .309)

And the next corner is located at (cos (306), sin (306))  = about (.588, -.809)

And by symmetry, the final two corner points are located at  (-.588, -.809)  and (-.951, .309)

Here's what it kinda' looks like ..... (fig. 2).........http://www.cut-the-knot.org/pythagoras/pentagon.shtml

And here's a graph of the points......I'll leave it to you to "connect the dots".......https://www.desmos.com/calculator/rabbm7mnln

CPhill  May 28, 2015
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#1
+91432
0

You need to expand this question

Melody  May 28, 2015
#2
+80866
+10

I'm assuming the "star" can be fashioned out of a pentagon inscribed in a circle having a radius of 1.  And the center of this circle is located at (0, 0).

I'm also assuming that the "top" corner (vertex) of the star is located at (0,1)

Then.......proceeding clockwise, the next corner (vertex)  is located at (cos (18), sin (18))  = about (.951, .309)

And the next corner is located at (cos (306), sin (306))  = about (.588, -.809)

And by symmetry, the final two corner points are located at  (-.588, -.809)  and (-.951, .309)

Here's what it kinda' looks like ..... (fig. 2).........http://www.cut-the-knot.org/pythagoras/pentagon.shtml

And here's a graph of the points......I'll leave it to you to "connect the dots".......https://www.desmos.com/calculator/rabbm7mnln

CPhill  May 28, 2015
#3
+91432
0

Thanks Chis,  you make a lovely 5 point star

Melody  May 28, 2015
#4
+80866
+5

Well......I'm waiting for my "Gold Star"  for that one  !!!!

CPhill  May 28, 2015
#5
+91432
+5

Here is you Gold Star - you deserve it !!

Here are my gold stars

Melody  May 28, 2015
#6
+80866
0

# How did you end up with more stars than me when I answered the question ??????

CPhill  May 28, 2015
#7
+91432
+5

# How did you end up with a shiny red car!

Melody  May 28, 2015
#8
+80866
+5

# You're having wine  !!!!

CPhill  May 28, 2015
#9
+91432
0

I am not yet....    But it is an excellent idea :))

Actually that is true ---- I do have a shiny new red car !      (newer than me anyway    LOL )

Melody  May 28, 2015

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