Ronan

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14 years, 148 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are answers submitted by Ronan

Would this work for you?

q := r -> piecewise(0 <= r and r < 0.1*Unit(`mm`), 5*Unit((`kW`)/`m`^2));

It prits to pdf ok for me on Windows 10.

On windows  pagesetup is under File, Print and the are threee options.  Print, Print Preview and Page Setup.

Edit:- Maybe I misunderstood your question on the page layout and showing page break at about 80%. If you mean this icon I had a problem with it on the page break. Tried everything to fix it in page setup. Eventually I used Maple 2023 where it works ok, to print the documents. It must be a bug.

This gives solutions. The oupput looks messy though. 

eq := 2^x*(2 + sqrt(3))^x - 2*(1 + sqrt(3))^x = 2

solve(eq, x)

allvalues(%)

See solve details - Maple Help   for more information.

I can find integer values for the vertex coordinates and the angle bisector.  Could not find side lengths with integer values.

restart

with(LinearAlgebra); with(plots); with(plottools)

v1 := `<,>`(a, b)

Vector[column](%id = 36893489400601263868)

(1)

v2 := `<,>`(c, d)

Vector[column](%id = 36893489400601251100)

(2)

v3 := v2-v1

Vector[column](%id = 36893489400601245804)

(3)

v4 := `<,>`(e, f)

Vector[column](%id = 36893489400601240868)

(4)

Non*Isosceles

Eq1 := v1[1]^2+v1[2]^2 <> v2[1]^2+v2[2]^2

a^2+b^2 <> c^2+d^2

(5)

Eq2 := v1[1]^2+v1[2]^2 <> v3[1]^2+v3[2]^2

a^2+b^2 <> (c-a)^2+(d-b)^2

(6)

Eq3 := v2[1]^2+v2[2]^2 <> v3[1]^2+v3[2]^2

c^2+d^2 <> (c-a)^2+(d-b)^2

(7)

"Dot product of 2 vectors <>0 if they are not perpendicular  "

Eq4 := `assuming`([v1.v2 <> 0], [real])

a*c+b*d <> 0

(8)

Eq5 := `assuming`([simplify(v1.v3 <> 0)], [real])

-a^2+a*c-b^2+b*d <> 0

(9)

Eq6 := `assuming`([simplify(v2.v3 <> 0)], [real])

-a*c-b*d+c^2+d^2 <> 0

(10)

Angle*bisector

Eq7 := v1+alpha*(v2-v1) = v4

Vector[column](%id = 36893489400642032932) = Vector[column](%id = 36893489400601240868)

(11)

Eq8 := a+alpha*(a-c) = e

a+alpha*(a-c) = e

(12)

Eq9 := b+alpha*(b-d) = f

b+alpha*(b-d) = f

(13)

"dot product of two vectors = the magnitude times the cos of the angle between them.  angle between v1 and v4 = angle between v2 and v4  Here  I have squared the dot product to remove square roots  "

Eq10 := `assuming`([(v1.v4)^2 = ((v1[1]^2+v1[2]^2)*(v1[1]^2+v1[2]^2))*cos^2*theta], [real])

(a*e+b*f)^2 = (a^2+b^2)^2*cos^2*theta

(14)

Eq11 := `assuming`([(v2.v4)^2 = (v2[1]^2+v2[2]^2)*(v1[1]^2+v1[2]^2)*cos^2*theta], [real])

(c*e+d*f)^2 = (c^2+d^2)*(a^2+b^2)*cos^2*theta

(15)

"Eliminate cos^(2)theta from Eq10 and Eq11"

NULL

Eq12 := `assuming`([(v1.v4)^2/((v1[1]^2+v1[2]^2)*(v4[1]^2+v4[2]^2)) = (v2.v4)^2/((v2[1]^2+v2[2]^2)*(v4[1]^2+v4[2]^2))], [real])

(a*e+b*f)^2/((a^2+b^2)*(e^2+f^2)) = (c*e+d*f)^2/((c^2+d^2)*(e^2+f^2))

(16)

````

sol := isolve({Eq1, Eq12, Eq2, Eq3, Eq4, Eq5, Eq6})

{a = _Z1*((1/2)*(_Z1*_Z2^2-_Z1*_Z3^2+1)*_Z2/_Z3-(1/2)*(_Z1*_Z2^2-_Z1*_Z3^2+1)*_Z3/_Z2+2*_Z1*_Z2*_Z3), b = _Z1, c = (1/2)*(_Z1*_Z2^2-_Z1*_Z3^2+1)/(_Z2*_Z3), d = _Z1, e = _Z2, f = _Z3}, {a = _Z2*_Z1, b = _Z1, c = _Z2, d = 1, e = _Z4, f = _Z5}

(17)

NULL

"Pick some values for Z1, 2, 3  "

sol1 := eval(sol, [_Z1 = 1, _Z2 = 1, _Z3 = 1])

{a = 2, b = 1, c = 1/2, d = 1, e = 1, f = 1}, {a = 1, b = 1, c = 1, d = 1, e = _Z4, f = _Z5}

(18)

assign(sol1[1])

evala(v1)

Vector[column](%id = 36893489400647704572)

(19)

evala(v2)

Vector[column](%id = 36893489400647706492)

(20)

evala(v3)

Vector[column](%id = 36893489400647708412)

(21)

evala(v4)

Vector[column](%id = 36893489400647710348)

(22)

evala(Eq12)

9/10 = 9/10

(23)

"Scale the points by a factor of 2 to get integers"

display(line(`<,>`(0, 0), 2*evala(v1)), line(`<,>`(0, 0), 2*evala(v2)), line(2*evala(v1), 2*evala(v2)), line(`<,>`(0, 0), 2*evala(v4)), scaling = constrained)

 

Eq8

2+(3/2)*alpha = 1

(24)

"(->)"

alpha = -2/3

(25)

eval(evala(Eq7), alpha = -2/3)

Vector[column](%id = 36893489400647799740) = Vector[column](%id = 36893489400647799620)

(26)

``

Download 2025-11-22_A_Special_Triangle.mw

  This might help. In Maple 2024 under Format Styles  you can alter the font and other settings. Different Styles sets can be exported and imported using Manage Styles Sets.

I am not exactly sure frm you wording of "k consecutive random characters". Is this what you want?

restart

NULL

randomize

randomize

(1)

[seq(StringTools:-Char(i), i = 30 .. 128)]

["", "", " ", "!", """, "#", "$", "%", "&", "'", "(", ")", "*", "+", ",", "-", ".", "/", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", ":", ";", "<", "=", ">", "?", "@", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z", "[", "\", "]", "^", "_", "`", "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "{", "|", "}", "~", "", "�"]

(2)

num := rand(30 .. 128)

proc () (proc () option builtin = RandNumberInterface; end proc)(6, 99, 7)+30 end proc

(3)

k := 25

25

(4)

[seq(StringTools:-Char(num()), i = 1 .. k)]

["O", "L", "%", "K", "I", "&", "j", "X", "-", "", "c", "j", "D", "y", "d", "`", "k", "P", "R", ")", "0", "\", "E", "w", " "]

(5)

NULL

Download 2025-10-12_A_Random_Characters.mw

You can do this .

evalc(D11)

To get real part only.

evalc(Re(D11))

Or imaginary part only.

evalc(Im(D11))

It i seasiest to use Equal fr0m the LlinearAlgebra package for this.

V1 := <2, 3, -7>;
                             [    2     ]
                             [          ]
                       V1 := [    3     ]
                             [          ]
                             [&uminus0;7]

V2 := <2, 3, -7>;
                             [    2     ]
                             [          ]
                       V2 := [    3     ]
                             [          ]
                             [&uminus0;7]

Equal(V1, V2);
                              true

The is something to do with how maple evaluates Vectors and Matrices.  delay evaluation quotes  '...... help here. There may be nicer ways to do this though.

{'Matrix'([1])} union {'Matrix'([1])};
                         {Matrix([1])}

eval({'Matrix'([1])} union {'Matrix'([1])});
                             {[1]}



 

One of your simpler puzzles. 

restart

NULL

NULL

A := Matrix(4, 7, {(1, 1) = 343, (1, 2) = 0, (1, 3) = 15625, (1, 4) = 0, (1, 5) = 32, (1, 6) = 0, (1, 7) = 36, (2, 1) = 0, (2, 2) = x, (2, 3) = 0, (2, 4) = 15657, (2, 5) = 0, (2, 6) = 68, (2, 7) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 31625, (3, 4) = 0, (3, 5) = y, (3, 6) = 0, (3, 7) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = z, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0})

Matrix(%id = 36893489885763238716)

(1)

The rows appear to be sums of of pairs above.

x := A[1, 1]+A[1, 3]

15968

(2)

x+A[2, 4]

31625

(3)

y := A[2, 4]+A[2, 6]

15725

(4)

z := A[3, 3]+y

47350

(5)

evalm(A)

array( 1 .. 4, 1 .. 7, [( 4, 5 ) = (0), ( 1, 2 ) = (0), ( 2, 4 ) = (15657), ( 1, 5 ) = (32), ( 1, 6 ) = (0), ( 3, 6 ) = (0), ( 1, 3 ) = (15625), ( 3, 4 ) = (0), ( 3, 2 ) = (0), ( 2, 3 ) = (0), ( 4, 2 ) = (0), ( 4, 1 ) = (0), ( 1, 1 ) = (343), ( 3, 7 ) = (0), ( 2, 2 ) = (15968), ( 4, 6 ) = (0), ( 2, 1 ) = (0), ( 2, 6 ) = (68), ( 2, 5 ) = (0), ( 2, 7 ) = (0), ( 1, 7 ) = (36), ( 4, 3 ) = (0), ( 1, 4 ) = (0), ( 3, 1 ) = (0), ( 3, 5 ) = (15725), ( 4, 4 ) = (47350), ( 4, 7 ) = (0), ( 3, 3 ) = (31625)  ] )

(6)

NULL

Download 5-05-25_A_sums.mw

This works. Nothing fancy.

plot(rhs(sol_1),x=0.15..5)

If the file doesn't use new features it willl open with a warning that it was created in a newer version of Maple. It should run ok. I opened one from a 2025 answer earlier.

9/2=4.5   Gives a similar triangle to the yellow one

sqrt(4.5/2)=sqrt( 2.25)=1.5   square root of ratio of areas gives sides ratio

(1.5+1)^2*2=12.5 ( total ratio of side length to mid point)^2 times yellow area gives size of triangle to midpoint of side AD.

12.5+12.5-2 =23 (green area)  

For some reason I can't upload the worksheet.
It is just the 3,4,5 triangle.

restart

sph:=(x-3)^2+(y-7)^2+(z-4)^2-25

plxy:=z=0
plyz:=x=0
ctr:=[3,7,4]
R:=5
ctrplxy:=[3,7,0]
4^2+Rxy^2=5^2
fsolve( ?? );
Rxy:=3
ctrplyz:=[0,7,4]
3^2+Ryz^2=5^2

fsolve( ?? );
Ryz:=4
#Center  and Radius on xy plane
ctrplxy;
Rxy
#Center  and Radius on yz plane
ctrplyz;
Ryz

This is just a quick test. I drew it in a CAD system to see. And  another possible assumption is the side slopes are equal.

 

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