Posts - MaplePrimes

MRB Constant X

by: Marvin Ray Burns 550 Product: Maple

April 21 2012

0 4

The MRB constant is evaluated by

Visualizing Sorting Algorithms

by: Clare So 175 Product: Maple 16

April 20 2012

9 4

I did not come across with a sorting algorithm animation that allows me to enter my own data, so I decided to write one in Maple.

In this worksheet, you can create an animation on sorting the integers that you have entered. If you let the worksheet to generate the data for you, you can specify the sortedness of the data. This feature allows you to visualize how some algorithms perform better or worse on data of a certain characteristic: The time complexity may not be...

MRB Constant W

by: Marvin Ray Burns 550

April 14 2012

0 1

proc (x) options operator, arrow; sum((-1)^n*(n^(1/n)-1), n = x .. infinity) end proc

(1)

What are the quotients ot the continued fration of the sum of

Here are the quotients of some partial sums.

$cfrac(evalf(sum(f(x), x = 1 .. 2)), 'quotients')$

(2)

$cfrac(evalf(sum(f(x), x = 1 .. 3)), 'quotients')$

(3)

$cfrac(evalf(sum(f(x), x = 1 .. 4)), 'quotients')$

(4)

$cfrac(evalf(sum(f(x), x = 1 .. 5)), 'quotients')$

(5)

$cfrac(evalf(sum(f(x), x = 1 .. 6)), 'quotients')$

(6)

$cfrac(evalf(sum(f(x), x = 1 .. 7)), 'quotients')$

(7)

$cfrac(evalf(sum(f(x), x = 1 .. 8)), 'quotients')$

(8)

$cfrac(evalf(sum(f(x), x = 1 .. 9)), 'quotients')$

(9)

$cfrac(evalf(sum(f(x), x = 1 .. 100)), 'quotients')$

(10)

$cfrac(evalf(sum(f(x), x = 1 .. 200)), 'quotients')$

(11)

$cfrac(evalf(sum(f(x), x = 1 .. 400)), 'quotients')$

(12)

$cfrac(evalf(sum(f(x), x = 1 .. 800)), 'quotients')$

(13)

$cfrac(evalf(sum(f(x), x = 1 .. 1600)), 'quotients')$

(14)

Here are the quotients of the continued fration of the sum.

$cfrac(evalf(sum(f(x), x = 1 .. infinity)), 'quotients')$

(15)

With the exception of the leading 0, that is close to the integer squence of pi.

(16)

The exponents of 2 that sum the numerator and denominator, in the following way, of that multiple of pi give rise to the integer sequences {0,1,2,3,8,16},numbers such that floor[a(n)^2 / 7] is a square, and {0,2,3,4,8,16},{0,3} union powers of 2.

evalf((2^16-2^8-2^5-2^2-2-2^0)*Pi/(2^16-2^8-2^4-2^3-2^2-2^0))

(17)

We can do the same thing for the first 20 quotients giving rise to the integer sequences {0,1,2,5,6,8,10,13,17,19,22,23,24,28,31} and {0,4,6,9,12, 14,15,16,18,22, 23,24,28,31}. What can be said of these sequences?

$cfrac(evalf(sum(f(x), x = 1 .. infinity), 20), 20, 'quotients')$

(18)

(19)

evalf((2^31-2^28-2^24-2^23-2^22-2^19-2^17-2^13-2^10-2^8-2^6-2^5-2^2-2-2^0)*Pi/(2^31-2^28-2^24-2^23-2^22-2^18-2^16-2^15-2^14-2^12-2^9-2^6-2^4-2^0), 20)

(20)

Newton-Raphson Fractal Black Areas Revealed

by: HSybesma 20

April 04 2012

4 3

NewtonBlackArea.mw

I have been working with Newton-Raphson fractals for some time. Like others it was necessary to deal with the "black areas" many times, so I performed some additional analysis and present some of these results here. This will allow others to stop coloring these areas black and allow visualization of the structure inside these areas. It will also help demonstrate...

Extension of getdata

by: Markiyan Hirnyk 7809 Product: Maple

April 03 2012

2 4

Starting from Maple 15, the useful ?plottools/getdata command is added. It tansforms a Maple plot to a Matrix. Unfortunately, the getdata command deals only with Maple plots. The question arises: "How to get a data from bmp, jpg, tiff, pcx, gif, png and wmf formats?" This is used in medicine and engineering. Such question was asked here

Trial ZNO in Maple 16

by: Valery Cyboulko 160 Product: Maple 16

April 02 2012

3 2

2012.zip

Ukraine. External independent evaluation (ZNO) in 2012. Trial in Maple 16.

html 3-interactive in Ukrainian: zno.zip

Maple 16 and Pasta

by: John May 3036 Product: Maple 16

March 29 2012

12 3

One of my coworkers brought in G.L. Legendre's book "Pasta By Design" (amazon.ca/dp/0500515808). It is full of photographs and parametric equations for 92 shapes of pasta. Of course, we had to set about plotting his equations in Maple. Orginally I was going to post about this before Maple 16 came out, but I was struck with how much better plots looked in the Maple 16 pre-release and so I decided to wait. As one example, here are the parametric equations for Giglio Ondulato noodles plotted using the default 3D plot settings in Maple 16 and Maple 15.

Maple 16 is here!

by: laurent 1020 Product: Maple

March 28 2012

20 14

Released today, with over 4500 additions and enhancements, Maple 16 reinforces our track record for consistent innovation and industry leadership in areas like ease of use and symbolic computing performance.

MRB Constant V

by: Marvin Ray Burns 550 Product: Maple

March 23 2012

0 2

The*MRB*constant = sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity) and sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity) = sum((-1)^n*(n^(1/n)-1), n = 2 .. infinity)

But what can we say about

(∏)(-1)^(n)*(n^(1/(n))-1)?

Maple does not evaluate it:

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. infinity))

product: Cannot show that (-1)^n*(n^(1/n)-1) has no zeros on [2,infinity] product((-1)^n*(n^(1/n)-1), n = 2 .. infinity)

(1)

And perhaps it should not because of the alternating sign;

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^2))

(2)

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^3))

(3)

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^3+1))

(4)

Download 3232012.mw

Bug in integrals of absolute value

by: Doug Meade 3088 Product: Maple 15

March 20 2012

1 13

A common example to emphasize that it is not OK to bring absolute values inside the integral compares

abs( int( cos(n*x), x=0..Pi ) ) asuming n::integer

and

int( abs( cos(n*x) ), x=0..Pi ) assuming n::integer

Maple correctly formulates the first to 0. But the second expression gives it more trouble, returning two messages:

Warning, unable to determine if (1/2)*Pi*(1+2*_Z7)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option
Warning, unable to determine if (1/2)*Pi*(1+2*_Z8)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option

Rebound Rumble: That's a Wrap!

by: myGL 190

March 19 2012

4 0

Dr. Gilbert Lai is a mentor for the FIRST Robotics team SWAT 771. He is helping an all girls team from grades 7-12 design a basketball-shooting robot for this year’s annual FIRST Robotics Competition. Dr. Lai is using MapleSim and Maple to help the team understand the principles involved and design their robot. This blog post is part of a series that chronicles the progress of the team. Posts in the series include:

Part 1 - ...

MRB constant U

by: Marvin Ray Burns 550 Product: Maple

March 18 2012

0 0

If you use all the convergents of the simple continued fraction of the MRB constant as the terms of a generalized continued fraction, then likewise use the new convergents in another generalized continued fraction, and so on... you arrive at 0.5557531.... For more on this process see https://oeis.org/wiki/Convergents_constant .

Geometric interpretation of correlation and regres...

by: longrob 1409 Product: Maple

March 09 2012

7 4

I was introduced to the geometric interpretation of correlation and linear regression recently.

Orignially due to the famous statistician R.A.Fisher, the idea is that the correlation between
two variables is the cosine of the angle between the 2 vectors in n-dimensional space.
This can be demonstrated in Maple as follows:

First, we represent each variable as a vector and transform it so that it is centred at its
mean and has a length equal...

Google Insights and Maple

by: Christopher2222 6030 Product: Maple

March 07 2012

1 1

This should be a blog post but there is no option for ordinary mapleprimers.

If you have a gmail account you can access the data on google insights (what people search for on google and where in the world is that keyword searched the most). Actually you don't need gmail but you don't get access to the full data and your limited to a few searches. Using Maples internet connectivity commands I'm sure could prove to create some interesting apps.

Mechanics of Materials Toolbox for Maple

by: S.Arlou 117 Product: Maple

February 24 2012

2 1

Mechanics of Materials Toolbox Screencasts:

http://youtu.be/czz_uw0918E

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MaplePrimes Posts

MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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MRB Constant X

Visualizing Sorting Algorithms

MRB Constant W

Newton-Raphson Fractal Black Areas Revealed

Extension of getdata

Trial ZNO in Maple 16

Maple 16 and Pasta

Maple 16 is here!

MRB Constant V

Bug in integrals of absolute value

Rebound Rumble: That's a Wrap!

MRB constant U

Geometric interpretation of correlation and regres...

Google Insights and Maple

Mechanics of Materials Toolbox for Maple

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MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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