Experimenting with fractions

Fractions are very frequently used.  This is the form for a fraction:

    \[\frac{numerator}{denominator}\]

Let’s use it to express some commonly used fractions for \pi:

    \[30\degree\]

    \[\frac{22}{7}\]

    \[\frac{355}{113}\]

    \[\frac{104348}{33215}\]

Let’s get a little more complicated:

    \[\pi=\frac{22}{7}\]

    \[\pi=\frac{355}{113}\]

    \[\pi=\frac{104348}{33215}\]

And a little more …:

    \[\pi=\frac{22}{7}\]

    \[=\frac{355}{113}\]

    \[=\frac{104348}{33215}\]

And now, let’s align the three equal signs:

    \begin{align*} \displaystyle \pi&=\frac{22}{7}    \nonumber \\ &=\displaystyle \frac{355}{113}   \nonumber \\ &=\displaystyle \frac{104348}{33215} \end{align*}

 

Resolve the following partial fraction:

    \[\frac{1+x}{2+x}\]

Continue reading “Experimenting with fractions”

Acknowledgements

I’d like to thank the people who have made The Mathematics Digital Library possible.  The Mathematics Digital Library is experimental, and there is no “budget” for it in any sense of the word.  The people who put in the work to make it possible are my ex-students, and they help out voluntarily.  They contribute because like me, they have the vision that knowledge should be made freely available, and not locked in books stored in the closed stacks of libraries.  I am extremely grateful for the work they put into this project.

Joan Wee is a librarian at Nanyang Technological University, and she is responsible for the setting up WordPress (she is a WordPress wizard!), and for installing all the WordPress plug-ins used on the site.  She also introduced me to Latex.  Joan is passionate about the Japanese language, and is a frequent visitor to Japan.  She also volunteers at the Singapore Association for the Deaf, and at the Singapore Society for the Prevention of Cruelty to Animals.

Don Chai is very good at anything “technical”, and he provided the initial server space, and is the person behind OpenlySolved.org.  Don is from Bukit Mertajam, and works at SingTel.

Yupa Duangphim helped out with the bibliographic references in Thai language.  She is a librarian at the Khon Kaen University Library.

Three Master of Science (Information Systems) students have agreed to work on The Mathematics Digital Library for their Critical Inquiry.

Wang Chenhang graduated from Nanjing University of Science and Technology in June 2015, majoring in software engineering.  During his four years as an undergraduate, Chenhang studied algorithm design, an amazing and magical world for him.  He won second prize in 2014 National Blue-bridge Cup Design Contest for Software and silver prize in 2013 Invitational ACM-ICPC (Nanjing District).

Zhu Jingyang is enthusiastic and energetic.  She obtained a bachelors degree in Software Engineering from East China Normal University in 2014.  During her university life, she participated in a few mathematical modelling competitions which made her more interested in the process of knowledge acquiring and problem solving. After that, due to her love for this field, she started her work as consultant and business analyst.  She is now in Singapore to explore new opportunities here.

Zhang Jiaqi is a creative student from China.  He graduated from The State University of New York at Binghamton with bachelor degree in Electrical Engineering in May, 2015.  Because of his outstanding achievement during his candidature, Jiaqi was awarded ‘Magna Cum Laude’ at the graduation ceremony.  During the university life, he won the fall 2014 Undergraduate Award to Support Research and Creative Work by Undergraduate Research Center of State University of New York at Binghamton, and was selected as a research project assistant for a State University of New York at Binghamton faculty member’s research program by S3IP Undergraduate Research Initiative.  An outcome of this research was a paper he presented at the MicroTas 2015 conference entitled ‘Origami Paper-Based Microbial Fuel Cells for Disposable Biosensor’.  Jiaqi is in the Wee Kim Wee School of Communication and Information to further his interests in the information field.

Pavel Holoborodko developed QuickLatex, a WordPress plugin which renders the mathematics expressions beautifully on the Web.  All the equations you see on The Mathematics Digital Library are rendered using QuickLatex.

The tables were created using the Tables Generator.  This very useful tool creates tables in various formats.

The Mathematics Digital Library is hosted by Vodien (not for free although I have asked them if they would several times already), and I am grateful they keep the server up most of the time.