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Have a graph at desmos, but an unable to make the circles always intersect each other.

Request the missing logic (in the form of condition) that would enforce the two circles to always intersect only.

Edit Have implemented comment by @fleablood at https://www.desmos.com/calculator/7xmcap1o6r, but seems ineffective. May be my implementation is wrong.

jiten
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    You need the distance between the two centers to be less than the sum of the radii. You also need the the sum of the distance between the centers and one of the radii must be more than the other radii. – fleablood Apr 21 '18 at 04:49

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You are not having a mathematical problem but rather a how to use desmos problem.

$$|r_1-r_2| \le \|P_1-P_2\|_2\le r_1+r_2$$

should be the right constraint but note that typing a constraint in a single entry does not impose any constraint on the curves.

This is a modification of your code such that the circles are only plotted when they intersect.

Siong Thye Goh
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  • I hope that the last two conditions mean nothing in isolation. Hence, their removal will not affect anything, as at: https://www.desmos.com/calculator/jv889rkzge. But, feel that there is a difference in running of this (after removal of last two conditions) graph, vs your graph. May be I am wrong, but impression on running is like that. Have a further request to draw line joining the two centers when the circles intersect (or may be, for all cases). I tried but failed many times, and could achieve only a line through origin, with a proper slope, but that does not pass through the two centers. – jiten Apr 21 '18 at 07:59
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    here – Siong Thye Goh Apr 21 '18 at 08:06
  • Sorry, but could not work. Request help on desmos related 2 issues: (i) remember arc length to simulate arc movement by compass, as want to get length $AB$ copied to make perpendicular bisector of it, as by compass (https://www.desmos.com/calculator/37cxv0rubj). I could get only: https://www.desmos.com/calculator/uha63ysrvy; but not sure even if it is correct way. Feel (https://www.desmos.com/calculator/dwijmtdi0x) should on processing further should work, but need compute 3rd equidistant point rather than arbitrary one. (ii) How plot polar form $r= ae^{i\theta}=a(\cos\theta + i \sin\theta)$. – jiten Apr 24 '18 at 11:20
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    might take days for me to get back to you. is your problem a maths problem or a how to use a software problem? – Siong Thye Goh Apr 24 '18 at 15:43
  • Sorry for being late. It is just a software problem(issue), i.e. desmos. Unable to use it for two applications. – jiten Apr 24 '18 at 16:45
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    not an expert in using desmos, you might like to ask on their website.. i can look at your problem when i m freer a few days later. – Siong Thye Goh Apr 24 '18 at 16:51
  • Have made something for above issue (i): https://www.desmos.com/calculator/rrpjremiff. Please vet it, as it is not working for $h_1 \approx 4.6$ and further properly. But, issue (ii) is confusing as seemingly should need polar graph with radians, and then confuse out in trying to work out $e^{i\theta}$. – jiten Apr 25 '18 at 05:40
  • I want to request your help for the above issue (i) with a modified diagram at : https://www.desmos.com/calculator/c1h3qhqkeu. I want to know that the function $6$ is equivalent to taking ruler. Also, request help in $3$ issues: issue (1): find error in function $6$, as full length of line segment joining two intersection points of two circles is not showing up. Issue (2): negative coordinates (either $x,y$) of any of the two points ($A,B$) give error in construction. Issue (3): Also, for positive coordinates of $A,B$, there is additional arc display. – jiten Apr 25 '18 at 12:06
  • I have posted a new question with issue (i) above at : https://math.stackexchange.com/q/2753088/424260. Please help. – jiten Apr 25 '18 at 12:21
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    hectic period for me... still days to go before i can tackle any indirect/long questions... – Siong Thye Goh Apr 25 '18 at 17:12
  • Please help with a smaller problem made by modifying the issue (i) by drawing two circles with polar coordinates $z= re^{i\theta}$. Have an attempt at : https://www.desmos.com/calculator/kivpmwjz5z. Please edit it so that it works, by having the centre specified for both circles. As maximum intersection is half of length of line segment $AB$, with the angle with both ends to the two intersection points on the lune being $60^0$. The minimum angle made by either center may be $\approx 1^0$. This way algebraic calculations needed in earlier attempt would not be needed to compute intersection pts. – jiten Apr 25 '18 at 23:34
  • no time today... also if its' a software prob... try stackoverflow... faster response... – Siong Thye Goh Apr 25 '18 at 23:34
  • It is not a software issue, it is just drawing complex number based two circles on polar diagram in desmos, with $\theta \in {0^0\cdots 60^0}$. The radius $r$ would be slightly more than half the length of the segment $AB$. Please draw one circle, rest I will try to attempt. Only one circle will be all I be asking for now. – jiten Apr 25 '18 at 23:36
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    get back to you in a few days... rushing things. – Siong Thye Goh Apr 25 '18 at 23:38
  • I want to add that numpy gives such a small graph that it is useless, as at: https://i.stack.imgur.com/Ef1SJ.png. Cannot see even what is happening. It is only desmos, that has some chance of viewing that too with knowledge of algebraic expression, and in that if could draw a circle with $z = re^{i\theta} = r(\cos \theta + i\sin\theta)$ (with range of values of $r, \theta$ known), then would be very helpful. I saw all books with solution manuals; but this basic knowledge to plot one circle in polar coordinates by specifying center is nowhere. Also, cannot specify in desmos $i = \sqrt{-1}$. – jiten Apr 26 '18 at 02:17
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    please do not ask a new question in a comment. We do not want to hide question in comment on this site. – Siong Thye Goh Apr 27 '18 at 17:37
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    I am very confused.. what is the maths problem that you face? please start a new question if you have a maths problem and ask one exact precise question at a time. If it is not a maths question, this is not the right place to be. If you have a software problem, try stackoverflow. – Siong Thye Goh Apr 28 '18 at 05:41
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    I still not sure what you are asking , formula of circle is of the form of $r=a$. relevant graph if this is what is being requested, then it is really not maths. – Siong Thye Goh Apr 28 '18 at 06:03
  • I tried to place a new question, and read a lot in the process (as usual). Found that polar curve plotting is not still possible in desmos. So, it means that $z-c=re^{i\theta}$ cannot be plotted. My main issue was this only. I hope am correct. Have found gnuplot and will give time to it in future, as seems the best of all. So, the question is no more, which was to give a center coordinate, and specify an angle ($\theta$) range in $z -c = r(\cos\theta +i\sin\theta)$ in desmos. I will try in gnuplot later. Anyway, your approach to state $r=a$ confuses, as will only form circle through origin. – jiten Apr 28 '18 at 10:44