Tokoro

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Can Maple 2026 AI solve this question? The answer of 5 points on the circle is radius 7/sqrt(3) by 7,5,3,5,3 lengthes.
No one shows how to solve this by Maple.
I hope Maple 2026 can solve this. 
Tokoro.

@Tokoro The answer of 7 points. 

@Tokoro T. Suzuki find the minimum radius answers for points untill 24.

@Tokoro  This is new answer for 5 points. And this is the minimum r for 5 points. T. Suzuki find this answer.

Thanks Kitonum 19099 and sursumCorda 20.

Both methods solve this puzzle symbolically. 

Tokoro.


 

:RLC circuit I want to solve.

restart

with(DynamicSystems); with(inttrans)

E := 1; J := 3; R := 3; L := 1; C := 1/2

(1/s-6/s^2)/(s+3+2/s)

(1/s-6/s^2)/(s+3+2/s)

(1)

i__RL := proc (t) options operator, arrow; invlaplace((1/s-6/s^2)/(s+3+2/s), s, t) end proc

proc (t) options operator, arrow; invlaplace((1/s-6/s^2)/(s+3+2/s), s, t) end proc

(2)

"(->)"

-4*exp(-2*t)-3+7*exp(-t)

(3)

e__C := proc (t) options operator, arrow; E-i__RL(t)*R-L*(diff(i__RL(t), t)) end proc

proc (t) options operator, arrow; E-i__RL(t)*R-L*(diff(i__RL(t), t)) end proc

(4)

"(->)"

10+4*exp(-2*t)-14*exp(-t)

(5)

plot([-4*exp(-2*t)-3+7*exp(-t), 10+4*exp(-2*t)-14*exp(-t)], t = 0 .. 10, color = [red, blue], thickness = 3, labels = ["t", "i(t)_red and vc(t)_blue"])

 

NULL

(1/s-6/s^2)/(s+3+2/s)

(1/s-6/s^2)/(s+3+2/s)

(6)

Solve eq(6) by Maple's dsolve.

E := 1; R := 3; C := 1/2; L := 1; J := 3

sol := dsolve([L*(diff(diff(q(t), t), t))+R*(diff(q(t), t))+q(t)/C = 1-6*t, q(0) = 0, (D(q))(0) = 0])

q(t) = 2*exp(-2*t)-7*exp(-t)-3*t+5

(7)

rhs(q(t) = 2*exp(-2*t)-7*exp(-t)-3*t+5)

2*exp(-2*t)-7*exp(-t)-3*t+5

(8)

plot(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t), t = 0 .. 10, color = red, thickness = 3)

 

v[c] := proc (t) options operator, arrow; E-R*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t))-L*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t, t)) end proc

proc (t) options operator, arrow; E-R*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t))-L*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t, t)) end proc

(9)

(proc (t) options operator, arrow; E-R*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t))-L*(diff(2*exp(-2*t)-7*exp(-t)-3*t+5, t, t)) end proc)(t)

10+4*exp(-2*t)-14*exp(-t)

(10)

i__c := proc (t) options operator, arrow; diff(C*(10+4*exp(-2*t)-14*exp(-t)), t) end proc

proc (t) options operator, arrow; diff(C*(10+4*exp(-2*t)-14*exp(-t)), t) end proc

(11)

(proc (t) options operator, arrow; diff(C*(10+4*exp(-2*t)-14*exp(-t)), t) end proc)(t)

-4*exp(-2*t)+7*exp(-t)

(12)

plot([10+4*exp(-2*t)-14*exp(-t), -4*exp(-2*t)+7*exp(-t)], t = 0 .. 5, color = ["red", "blue"], thickness = 3, labels = ["t", "vc(t)_red,ic(t)_blue"])

 

NULL

NULL


 

Download DynamicSystem-How_to_ODE.mw

@Preben Alsholm It makes equation (7). And I want to solve this ODE in Eq.(7) by Maple.

Using laplace convertion, I can get the answer and can plot it.

@acer Thanks show me the power of Maple. 

@acer Thanks your follow up. I try to find the mimimum of the intersect. 

Optimization can find it. How to find by min(extrema....? 

 

Totoro.

plot-15-iPlot.mw 

@tomleslie x=45, y=45, intersect=2.117 may be the maximum of intersect. How to find this value by Maple?

The only one 3D mesh answer for "Make one ohm by one ohm."

The only one 2D mesh for "Make one ohm by one ohm".

Node 1 to 13 is 1/2 ohm made by one ohm, where each current is different.

 

@dharr @Carl Love is right. Surprisingly, both are planar. I only know this very fameous math problem. I only know the answers and don't know how to solve. I rewrited this math problem to the electric circuit problem.

Tokoro

Same question except make two ohm by one ohms, each current must different.

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