Ronan

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13 years, 138 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are answers submitted by Ronan

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.

 

On my pc Maple docs are here. Or are you asking about windows File History?

If memory serves me correctly, I think I specified Home User. As I have a Personal Edition license.

Hope this is correct
 

restart

L:=1

1

(1)

E:=[0,0]

[0, 0]

(2)

A:=[-1/2*L,L*sqrt(3)/2]

 

[-1/2, (1/2)*3^(1/2)]

(3)

D1:=[L,0]

[1, 0]

(4)

C:=[L,L]

[1, 1]

(5)

AC:=C-A

[3/2, -(1/2)*3^(1/2)+1]

(6)

AB:=L

1

(7)

BC:=L

1

(8)

expn1:=2*L*cos(theta)=sqrt(AC[1]^2+AC[2]^2)

2*cos(theta) = (1/2)*(9+4*(-(1/2)*3^(1/2)+1)^2)^(1/2)

(9)

theta:=solve(expn1,theta)

arccos((1/4)*(9+4*(-(1/2)*3^(1/2)+1)^2)^(1/2))

(10)

b:=2*Pi-(Pi-2*theta)

Pi+2*arccos((1/4)*(9+4*(-(1/2)*3^(1/2)+1)^2)^(1/2))

(11)

simplify( (11) );

2*Pi-2*arcsin((1/2)*(4-3^(1/2))^(1/2))

(12)

expn2:=L-L*cos(c)=L*sin(2*Pi/3)-L*sin(a+Pi/3)

1-cos(c) = (1/2)*3^(1/2)-sin(a+(1/3)*Pi)

(13)

expn3:=L-L*sin(c)=L*cos(2*Pi/3)+L(a+Pi/3)

1-sin(c) = 1/2

(14)

c:=solve(expn3,c)

(1/6)*Pi

(15)

a:=solve(expn2,a)

-(1/3)*Pi+arcsin(3^(1/2)-1)

(16)

simplify( (16) );

-(1/3)*Pi+arcsin(3^(1/2)-1)

(17)

B[1]:=L-L*sin(c)

1/2

(18)

B[2]:=L-L*cos(c)

-(1/2)*3^(1/2)+1

(19)

B:=[B[1],B[2]]

[1/2, -(1/2)*3^(1/2)+1]

(20)


plots:-display(plottools:-polygon([E,D1,C,B,A]),colour=yellow)

1

 

 

 


 

Download Fun-Angles.mw

In you expression

test := subs(a = 2, x^2/2 + x*a + a^2*ln(x - a))

ln(x-a) becomes complex with x<a.

I dont know is this is the Clifford package you mean. I found this on last friday. Index of /12/eng/files/st_files/kyrchei/kyr_files/Maple Package

You can set the number of digits displayed on the screen using for eample

interface(displayprecision=5)

This does not affect the accuracy of calculation set by Digits

I use 4k Video Downloader. There is a free version of it. AFAIK if you are not redestributing the videos so purely for you own use it is not a problem. 

There are  a couple you tube chanels I use. Insights into Mathematics and Wild Egg Maths. I downloaded most of the videos. About 3 weeks ago both chanels were hacked and all the content was gone.So far only Wild egg maths has been restored.

Basically if you value it get you own copy.

I tried setting transparency to 0 but that didn't work. I used plottools:-point as a work around.

L:=plottools:-line([0,0],[0,3],color="blue"):
c1:=plottools:-disk([0,1],.1):
c2:=plottools:-disk([0,2],.1,color="green",transparency=0):
c3:=plottools:-point([0,1],symbol=solidcircle,symbolsize=45,color="red");
plots:-display([L,c1,c2,c3],scaling=constrained,axes=none)

 

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