Archive for the ‘Mathematics’ Category

Weekly Link Roundup – 2

Links published on May 04, 2009:

Math world, simple mental calculations or what’s going on with education?

Most interesting math blog post I have read for a long time. Have a read guys and tell me how you find it.

Programmer Competency Matrix:

http://www.indiangeek.net/programmer-competency-matrix/

Panoramic Image & Viewer related resources:

http://krolik.net/PIV/
http://flashpanoramas.com/player/
http://www.mojavelinux.com/cooker/demos/panojs/
http://www.eurofresh.se/test/shockwpanos.htm
http://www.michielpost.nl/panorama/

File conversion utility for panoramic photos:

http://www.outerspace-software.com/bixorama.html

Automatic image stitching:

http://www.cs.ubc.ca/~mbrown/autostitch/autostitch.html

Panoramic Image App (Commercial):

http://www.autopano.net/

Panorama Gallery:

http://www.cs.ubc.ca/~mbrown/panogallery/panogallery.html

Panoramic Viewer:

http://s3.envato.com/files/4810/index.html

TDD Links:

http://codebetter.com/blogs/darrell.norton/articles/50337.aspx
A Conversation with Martin Fowler
Mocks Aren’t Stubs
Learn about .NET Unit Testing with Typemock

Old Version Downloads:

http://www.oldapps.com/

10 Youtube URL Tricks You Should Know About

http://www.makeuseof.com/tag/10-youtube-url-tricks-you-should-know-about/

100 Best JavaScript Resources

http://www.spoonfeddesign.com/100-best-javascript-resources

Performance killer: Disk I/O

http://nathanaeljones.com/11061_Performance_killer_Disk_I_O

Top 20 Best Agile Development Books, Ever

http://www.noop.nl/2008/06/top-20-best-agile-development-books-ever.html

Top 100 Best Software Engineering Books, Ever

http://www.noop.nl/2008/06/top-100-best-software-engineering-books-ever.html

Top 20 Programming Books

http://yaneshtyagi.blogspot.com/2008/04/top-20-programming-books.html

Top 10 Concepts That Every Software Engineer Should Know

http://blog.csdn.net/andylin02/archive/2008/07/26/2716304.aspx

Securing ASP.NET Applications

http://www.novologies.com/post/2009/04/08/Securing-ASPNET-Applications.aspx

The ADO.NET Entity Framework must read:

Introducing the Entity Framework [MSDN]
The ADO.NET Entity Framework Overview
ADO.NET Tech Preview: Entity Data Model

Introduction to the Entity Framework [Code Project]

Windows Communication Foundation must read:

Fundamental Windows Communication Foundation Concepts
What Is Windows Communication Foundation?

A Guide to Designing and Building RESTful Web Services with WCF 3.5

Howto Dynamically Insert Javascript And CSS:

This is a short and sweet little tutorial to show you how to dynamically insert a new Javascript (or style sheet) into your web pages, and explores how you can exploit cross-domain includes in your applications.

As JSON and DHTML start to get pushed more and more to the forefront of web-based applications, the web designer is faced with a new problem: how to dynamically insert a script element into an existing web page. It won’t take long to figure out that ajax loads and innerHTML injections won’t work.

http://www.hunlock.com/blogs/Howto_Dynamically_Insert_Javascript_And_CSS

Yahoo! Pipes and JQuery : Goodbye Same Origin Policy

http://www.badlydrawntoy.com/2008/07/08/yahoo-pipes-and-jquery-same-origin-policy/

URL Shorteners:

http://is.gd/
http://tr.im/
http://ow.ly/url/shorten-url
http://bit.ly
http://tinyurl.com

Interview Tips:

http://interviewtips.org/

LINQ to Entities:

http://www.linqdev.com/PublicPortal/publicportal/linq-to-entities.aspx

LINQ Learning Guide: LINQ to Entities

http://searchwindevelopment.techtarget.com/generic/0,295582,sid8_gci1299600,00.html

The ADO.NET Entity Framework Overview:

http://msdn.microsoft.com/en-us/library/aa697427(VS.80).aspx

Parallelism Videos Galore

http://blogs.msdn.com/pfxteam/

Writing LINQ Queries with the Entity Framework:

http://www.informit.com/articles/article.aspx?p=1237071

ASP.NET Dynamic Data Overview

http://msdn.microsoft.com/en-us/library/cc488546.aspx

Inheritance and Associations with Entity Framework Part 1

http://mosesofegypt.net/post/Inheritance-and-Associations-with-Entity-Framework-Part-1.aspx

Model Domain Objects with the Entity Framework

http://visualstudiomagazine.com/features/article.aspx?editorialsid=2425

Lambda the Ultimate : Programming Languages Weblog

http://lambda-the-ultimate.org/

Introduction to Domain Specific Languages

http://www.infoq.com/presentations/domain-specific-languages

Good blog site on Patterns:

http://blogs.msdn.com/erwinvandervalk/default.aspx

Pattern site on Hexagonal architecture

http://alistair.cockburn.us/Hexagonal+architecture

JSINQ – LINQ to Objects for JavaScript

http://www.codeplex.com/jsinq

JSINQ: LINQ style access for JavaScript objects

http://ajaxian.com/archives/jsinq-linq-for-javascript

LINQ to SQL: SQL-CLR Type Mismatches (LINQ to SQL)

http://msdn.microsoft.com/en-us/library/bb386909.aspx

LINQ to SQL : Object Identity (LINQ to SQL)

http://msdn.microsoft.com/en-us/library/bb399376.aspx

Most interesting math blog post I have read for a long time. Have a read guys and tell me how you find it.
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Messing around with the ‘ad infinitum’!

Anybody who has observed the The Ultimate Clock For Nerds properly would know that the 7th hour is designated specially. I know this is pretty elementary level high school stuff but something about this intrigued me. Hence, I am writing on this. Part of the equation had .9 with bar sign. We should remember by now that this is used to symbolize the “infinitely repeating decimals”. The outcome of this all is something like this:

9s_equals

Now let me manifest why it intrigued my mind. How can this be equal to 1. Here’s how it can be proved albeit in a generalized manner:

0.1111……. is 1/9 where … represents “one”‘s ‘ad infinitum’.
0.2222……. is 2/9
0.3333……. is 3/9 or 1/3 or 33 1/3%
0.4444……. is 4/9
0.5555……. is 5/9
0.6666……. is 6/9 or 2/9 or 66 2/3%
and so and so on…

until 0.9999……. is 9/9 or 1 whole. the reason for that is because 0.9999 goes on forever….

0.9999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999……

and so on.
It’s basically one and so it is considered that.
That’s why 0.6666……is 0.66
2/3 that’s 2/3 of 100 is 66.666666666666666666666666666666666666666666666666666666666666666666666…
you get the point.
So 0.99999…. = 9/9 = 1
Taking another route:

let, x = 0.9999…
Therefore, 10x = 9.9999…
Therefore, 10x – x = 9.9999… – 0.9999…
Therefore, 9x = 9
Hence, x = 1

Here’s the same proof albeit in a different & pictorial representation:

9s_algebra
9s_thirds
9s_elevenths
9s_sevenths

By the way, for the more mathematical minded of you, the mathematical equation of this is:

lim(m –> ∞) sum(n = 1)^m (9)/(10^n) = 1

Here’s one more discussion on the same:

http://www.curiousmath.com/index.php?name=PNphpBB2&file=viewtopic&t=48