text:
Engineering Acoustics/Transducers - Loudspeaker

=Acoustic transducer=

The purpose of an acoustic transducer is to convert electrical energy into acoustic energy. Many variations of acoustic transducers exist, such as electrostatic, balanced armature and moving-coil loudspeakers. This article focuses on moving-coil loudspeakers since they are the most commonly used type of acoustic transducer. First, the physical construction and principle of a typical moving coil transducer are discussed briefly. Second, electro-mechano-acoustical modeling of each element composing the loudspeaker is presented in a tutorial way to reinforce and supplement the theory on electro-mechanical analogies and electro-acoustic analogies previously seen in other sections. Third, the equivalent circuit is analyzed to introduce the theory behind Thiele-Small parameters, which are very useful when designing loudspeaker enclosures. A method to experimentally determine Thiele-Small parameters is also included.

Moving-coil loudspeaker construction and principle
The classic moving-coil loudspeaker driver can be divided into three key components:

1) The magnet motor drive system, comprising the permanent magnet, the center pole and the voice coil acting together to produce a mechanical force on the diaphragm from an electrical current.

2) The loudspeaker cone system, comprising the diaphragm and dust cap, permitting mechanical force to be translated into acoustic pressure;

3) The loudspeaker suspension, comprising the spider and surround, preventing the diaphragm from breaking due to over excursion, allowing only translational movement and tending to bring the diaphragm back to its rest position.

The following illustration shows a cut-away view of a typical moving coil-permanent magnet loudspeaker. A coil is mechanically coupled to a diaphragm, also called cone, and rests in a fixed magnetic field produced by a magnet. When an electrical current flows through the coil, a corresponding magnetic field is emitted, interacting with the fixed field of the magnet and thus applying a force to the coil, pushing it away or towards the magnet. Since the cone is mechanically coupled to the coil, it will push or pull the air it is facing, causing pressure changes and emitting a sound wave.

Figure 1: A cross-sectional view of a typical moving-coil loudspeaker

An equivalent circuit can be obtained to model the loudspeaker as a lumped system. This circuit can be used to drive the design of a complete loudspeaker system, including an enclosure and sometimes even an amplifier that is matched to the properties of the driver. The following section shows how such an equivalent circuit can be obtained.

Electro-mechano-acoustical equivalent circuit
Electro-mechanico-acoustical systems such as loudspeakers can be modeled as equivalent electrical circuits as long as each element moves as a whole. This is usually the case at low frequencies or at frequencies where the dimensions of the system are small compared to the wavelength of interest. To obtain a complete model of the loudspeaker, the interactions and properties of electrical, mechanical, and acoustical subsystems composing the loudspeaker driver must each be modeled. The following sections detail how the circuit may be obtained starting with the amplifier and ending with the acoustical load presented by air. A similar development can be found in [1] or [2].

Electrical subsystem
The electrical part of the system is composed of a driving amplifier and a voice coil. Most amplifiers can be approximated as a perfect voltage source in series with the amplifier output impedance. The voice coil exhibits an inductance and a resistance that may be directly modeled as a circuit.

Figure 2: The amplifier and loudspeaker electrical elements modeled as a circuit

Electrical to mechanical subsystem
When the loudspeaker is fed an electrical signal, the voice coil and magnet convert current to force. Similarly, voltage is related to the velocity. This relationship between the electrical side and the mechanical side can be modeled by a transformer.

$$ \tilde{f_c} = Bl \tilde{i} $$;         $$ \tilde{u_c} = \dfrac{\tilde{e}}{Bl} $$

Figure 3: A transformer modeling transduction from the electrical impedance to mechanical mobility analogy

Mechanical subsystem
In a first approximation, a moving coil loudspeaker may be thought of as a mass-spring system where the diaphragm and the voice coil constitute the mass and the spider and surround constitute the spring element. Losses in the suspension can be modeled as a resistor.

Figure 4: Mass spring system and associated circuit analogies of the impedance and mobility type.

The equation of motion gives us :

$$ \tilde{f_c} = R_m \tilde{u_c} + \dfrac{\tilde{u_c}}{ j \omega C_{MS}} + j \omega M_{MD} \tilde{u_c} $$

$$ \dfrac{\tilde{f_c} }{\tilde{u_c}}= R_m+\dfrac{1}{ j \omega C_{MS}}+ j\omega M_{MD} $$

Which yields the mechanical impedance type analogy in the form of a series RLC circuit. A parallel RLC circuit may also be obtained to get the mobility analog following mathematical manipulation:

$$ \dfrac{\tilde{u_c} }{\tilde{f_c}}= \dfrac{1}{R_m+\dfrac{1}{ j \omega C_{MS}}+ j\omega M_{MD} }$$

$$ \dfrac{\tilde{u_c} }{\tilde{f_c}}= \dfrac{1}{\dfrac{1}{G_m}+\dfrac{1}{ j \omega C_{MS}} + \dfrac{1}{\dfrac{1}{j \omega M_{MD}}}} $$

Which expresses the mechanical mobility type analogy in the form of a parallel RLC circuit where the denominator elements are respectively a parallel conductance, inductance, and compliance.

Mechanical to acoustical subsystem
A loudspeaker’s diaphragm may be thought of as a piston that pushes and pulls on the air facing it, converting mechanical force and velocity into acoustic pressure and volume velocity. The equations are as follow:

$$ \tilde{P_d} = \dfrac{\tilde{f_c}}{\tilde{S_D}} $$; $$ \tilde{U_c} = \tilde{u_c}{S_D}$$

These equations can be modeled by a transformer.

Figure 5: A transformer modeling the transduction from mechanical mobility to acoustical mobility analogy performed by a loudspeaker's diaphragm

Acoustical subsystem
The impedance presented by the air load on the loudspeaker's diaphragm is both resistive due to sound radiation and reactive due to the air mass that is being pushed radially but does not contribute to sound radiation to the far field. The air load on the diaphragm can be modeled as an impedance or an admittance. Specific values and approximations can be found in [1], [2] or [3]. Note that the air load depends on the mounting conditions of the loudspeaker. If the loudspeaker is mounted in a baffle, the air load will be the same on each side of the diaphragm. Then, if the air load on one side is $$ Y_{AR} $$ in the admittance analogy, then the total air load is $$ Y_{AR}/2 $$ as both loads are in parallel.

Complete electro-mechano-acoustical equivalent circuit
Using electrical impedance, mechanical mobility and acoustical admittance yield the following equivalent circuit, modeling the entire loudspeaker drive unit.

Figure 6: A complete electro-mechano-acoustical equivalent circuit of a loudspeaker drive unit

This circuit can be reduced by substituting the transformers and connected loads by an equivalent loading that would present the same impedance as the loaded transformer. An example of this is shown on figure 7, where acoustical and electrical loads and sources have been "brought over" to the mechanical side.

Figure 7: Mechanical equivalent circuit modeling of a loudspeaker drive unit

The advantage of doing such manipulations is that we can then directly relate electrical measurements with elements in the circuit. This will later allow us to obtain values for the different components of the model and match this model to real loudspeaker drivers. We can further simplify this circuit by using Norton's theorem and converting the series electrical components and voltage source into an equivalent current source and parallel electrical components. Then, using a technique called the Dot method, presented in section Solution Methods: Electro-Mechanical Analogies, we can obtain a single loop series circuit which is the dual of the parallel circuit previously obtained with Norton's theorem. If we are mainly interested in the low frequency behavior of the loudspeaker, as should be the case when using lumped element modeling, we can neglect the effect of the voice coil inductance, which has an effect only at high frequencies. Furthermore, the air load impedance at low frequencies is mass-like and can be modeled by a simple inductance $$M_{M1}$$. This results in a simplified low frequency model equivalent circuit, shown of figure 8, which is easier to manipulate than the circuit of figure 7. Note that the analogy used for this circuit is of the impedance type.

Figure 8: Low frequency approximation mechanical equivalent circuit of a loudspeaker drive unit

Where $$M_{M1} = 2.67 a^3 \rho $$ if $$ a $$ is the radius of the loudspeaker and $$ \rho $$, the density of air. Mass elements, in this case the mass of the diaphragm and voice coil $$M_{MS}$$ and the air mass loading the diaphragm $$2M_{M1}$$ can be regrouped in a single element:

$$ M_{MS} = M_{MD}+2M_{M1}$$

Theory
The complete low frequency behavior of a loudspeaker drive unit can be modeled with just six parameters, called Thiele-Small parameters. Most of these parameters result from algebraic manipulation of the equations of the circuit of figure 8. Loudspeaker driver manufacturers seldom provide electro-mechano-acoustical parameters directly and rather provide Thiele-Small parameters in datasheets, but conversion from one to the other is quite simple. The Thiele-Small parameters are as follow:

1. $$ R_e $$, the voice coil DC resistance;

2. $$ Q_{ES} $$, the electrical Q factor;

3. $$ Q_{MS} $$, the mechanical Q factor;

4. $$ f_s $$, the loudspeaker resonance frequency;

5. $$ S_D $$, the effective surface area of the diaphragm;

6. $$ V_{AS} $$, the equivalent suspension volume: the volume of air that has the same acoustic compliance as the suspension of the loudspeaker driver.

These parameters can be related directly from the low frequency approximation circuit of figure 8, with $$ R_e $$ and $$ S_D $$ being explicit.

$$ Q_{MS} = \dfrac{1}{R_{MS}} \sqrt{\dfrac{M_{MS}}{C_{MS}}} $$; $$ Q_{ES} = \dfrac{R_g + R_e }{(Bl)^2} \sqrt{\dfrac{M_{MS}}{C_{MS}}} $$ ; $$f_s= \dfrac{1}{2\pi\sqrt{M_{MS}C_{MS}}}$$; $$V_{AS}= C_{MS}S_D^2\rho c^2$$

Where $$\rho c^2$$ is the Bulk modulus of air. It follows that, if given Thiele-Small parameters, one can extract the values of each component of the circuit of figure 8 using the following equations :

$$ C_{MS} = \dfrac{V_{AS}}{S_D^2 \rho c^2} $$; $$M_{MS}= \dfrac{1}{(2 \pi f_s)^2 C_{MS}}$$; $$R_{MS} = \dfrac{1}{Q_{MS}}\sqrt{\dfrac{M_{MS}}{C_{MS}}}$$; $$Bl = \sqrt{\dfrac{R_e}{2 \pi f_s Q_{ES} C_{MS} } }$$; $$M_{MD}= M_{MS}-2M_{M1}$$;

Measurement
Many methods can be used to measure Thiele-Small parameters of drivers. Measurement of Thiele-Small parameters is sometimes necessary if a manufacturer does not provide them. Also, the actual Thiele-Small parameters of a given loudspeaker can differ from nominal values significantly. The method described in this section comes from [2]. Note that for this method, the loudspeaker is considered to be mounted in an infinite baffle. In practice, a baffle with a diameter of four times that of the loudspeaker is sufficient. Measurements without a baffle are also possible: the air mass loading will simply be halved and can be easily accounted for. The setup for this method includes an FFT analyzer or a mean to obtain an impedance curve. A signal generator of variable frequency and an AC meter can also be used.

Figure 9: Simple experimental setup to measure the impedance of a loudspeaker drive unit

$$ Z_{spk}= R\dfrac{V_{spk}}{V_s \left( 1-\dfrac{V_{spk}}{V_s} \right)} $$

Figure 10: A typical loudspeaker drive unit impedance curve

Once the impedance curve of the loudspeaker is measured, $$ R_e $$ and $$ f_s $$ can be directly identified by looking at the low frequency asymptote of the impedance value and the center frequency of the resonance peak. If the frequencies where $$Z_{spk}=\sqrt{R_e R_c}$$ are identified as $$f_l$$ and $$f_h$$, Q factors can be calculated.

$$ Q_{MS}= \dfrac{f_s}{f_h-f_l} \sqrt{\dfrac{R_c}{R_e}} $$

$$ Q_{ES} = \dfrac{Q_{MS}}{\dfrac{R_c}{R_e}-1} $$

$$S_D$$ can simply be approximated by $$\pi a^2 $$, where $$ a $$ is the radius of the loudspeaker driver. The last remaining Thiele-Small parameter, $$V_{AS}$$ is slightly trickier to measure. The idea is to either increase mass or reduce compliance of the loudspeaker drive unit and note the shift in resonance frequency. If a known mass $$M_x$$ is added to the loudspeaker diaphragm, the new resonance frequency will be:

$$f^'_s= \dfrac{1}{2 \pi \sqrt{(M_{MS} + M_x) C_{MS} } }$$

And the equivalent suspension volume may be obtained with:

$$V_{AS} = \left( 1- \dfrac{f^{'2}_s}{f_s^2} \right) \dfrac{S_D^2 \rho c^2}{(2 \pi f^'_s)^2 M_x}$$

Hence, all Thiele-Small parameters modeling the low frequency behavior of the loudspeaker drive unit can be obtained from a fairly simple setup. These parameters are of tremendous help in loudspeaker enclosure design.

Numerical example
This section presents a numerical example of obtaining Thiele-Small parameters from impedance curves. The impedance curves presented in this section have been obtained from simulations using nominal Thiele-Small parameters of a real woofer loudspeaker. Firsy, these Thiele-Small parameters have been transformed into an electro-mechano-acoustical circuit using the equation presented before. Second, the circuit was treated as a black box and the method to extract Thiele-Small parameters was used. The purpose of this simulation is to present the method, step by step, using realistic values so that the reader can get more familiar with the process, the magnitude of the values and with what to expect when performing such measurements.

For this simulation, a loudspeaker of radius $$a=6.55cm$$ is mounted on a baffle sufficiently large to act as an infinite baffle. Its impedance is obtained and plotted in figure 11, where important cursors have already been placed.

Figure 11: Simulated measurement of an impedance curve for a woofer loudspeaker

The low frequency asymptote is immediately identified as $$Re=6.6\Omega$$. The resonance is clear and centered at $$fs=33Hz$$. The value of the impedance at this frequency is about $$66\Omega$$. This yields $$\sqrt{R_eR_c}=20.8\Omega$$, which occurs at $$f_l=19.5 Hz$$ and $$f_h= 52.5 Hz$$. With this information, we can compute some of the Thiele-Small parameters.

$$ Q_{MS}= \dfrac{f_s}{f_h-f_l}\sqrt{\dfrac{R_c}{R_e}}=\dfrac{33}{52.5-19.5}*\sqrt{\dfrac{66}{6.6}}= 3.1 $$

$$ Q_{ES} = \dfrac{Q_{MS}}{\dfrac{R_c}{R_e}-1} = \dfrac{3.1}{\dfrac{66}{6.6}-1} = 0.35$$

As a next step, a mass of $$M_x=10g$$ is fixed to the loudspeaker diaphragm. This shifts the resonance frequency and yields a new impedance curve, as shown on figure 12.

Figure 12: Simulated measurement of an impedance curve for a woofer loudspeaker

$$S_{D} = \pi a^2 = 0.0135 m^2$$

$$V_{AS} = \left( 1- \dfrac{27.5^2}{33^2} \right) \dfrac{0.0135^2*1.18*344^2}{(2 \pi 27.5)^2*0.01}= 0.0272 m^3$$

Once all six Thiele-Small parameters have been obtained, it is possible to calculate values for the electro-mechano-acoustical circuit modeling elements of figure 6 or 7. From then, the design of an enclosure can start. This is discussed in application sections Sealed box subwoofer design and Bass reflex enclosure design.

=References=

[1] Kleiner, Mendel. Electroacoustics. CRC Press, 2013.

[2] Beranek, Leo L., and Tim Mellow. Acoustics: sound fields and transducers. Academic Press, 2012.

[3] Kinsler, Lawrence E., et al. Fundamentals of Acoustics, 4th Edition. Wiley-VCH, 1999.

[4] Small, Richard H. "Direct radiator loudspeaker system analysis." Journal of the Audio Engineering Society 20.5 (1972): 383-395.


text:
The Mojavi 3 Book

Introduction

 * 1) What Is Mojavi?
 * 2) Mojavi Features
 * 3) Benefits Of Using Mojavi

Getting Started

 * 1) Requirements
 * 2) Downloading Mojavi
 * 3) Installation
 * 4) Configuration
 * 5) Crash Course
 * 6) Creating Your First Module
 * 7) Migrating From Mojavi 2

Mojavi Architecture

 * 1) Core Components
 * 2) * Controller
 * 3) * Context
 * 4) * Request
 * 5) * User
 * 6) Directory Layout
 * 7) Naming Conventions
 * 8) Modules
 * 9) * Actions
 * 10) * Models
 * 11) * Templates
 * 12) * Views
 * 13) Configuration Files
 * 14) Diagrams
 * 15) * Application Flow
 * 16) * Filter Flow
 * 17) * Security
 * 18) * Validation

Beginning Mojavi 3

 * 1) Manipulating The Request
 * 2) * Files
 * 3) * Parameters
 * 4) Interprocess Communication
 * 5) Session Handling
 * 6) Database Interaction
 * 7) User Security
 * 8) * Securing Your Actions
 * 9) * What Is A Credential
 * 10) Filters
 * 11) * Pre-Execution
 * 12) * Post-Execution
 * 13) Validators
 * 14) * Parameter Validation
 * 15) Logging

Advanced Mojavi 3

 * 1) Integrating External Scripts
 * 2) Mojavi Exceptions
 * 3) Configuration Cache System
 * 4) Action Chains

Custom Components

 * 1) Registering
 * 2) Creating
 * 3) * Actions
 * 4) * Controllers
 * 5) * Filters
 * 6) * Loggers
 * 7) * Requests
 * 8) * Storages
 * 9) * Users
 * 10) * Views
 * 11) * Validators

Guides

 * 1) Separation of Logic
 * 2) Truly Modular Development

Tutorials

 * 1) Installing Mojavi 3
 * 2) Creating Your First Module
 * 3) Migrating From Mojavi 2.0
 * 4) Multi-Page Forms HOW-TO
 * 5) Global Templating - The Decorator Pattern
 * 6) Decorator Profiling
 * 7) Users And Security

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: The Mojavi 3 Book


text: Template:User blank-2

title: Template:User blank-2


text: Category:User pas

title: Category:User pas


text:
Talk:Rhetoric and Composition/Planning and Prewriting

Various talk
This is Old Word Wolf, again: I added a long, detailed section with genuine, classroom-tested strategies for finding a topic as part of the prewriting stage. My contribution was summarily deleted withing seconds without comment or notice as to why -- apparently a unilateral decision by one wikipedian. My contribution directly addressed the "dry" quality noted below, as well as getting quickly into the meat of the matter -- helping college students at the prewriting stage of locating a topic.

Further, the suggestion, later in the same section, of sending the freshman composition class writer to the library to research scholarly articles on Shakespeare would be laughable if it weren't so misguided. There is no faster way to discourage independent thinking and create a complete "writer's block" than by having a freshman try to sort out the gazillions of articles on just Hamlet or Julius Caesar or Midsummer Night's Dream, much less all the rest of the plays and sonnets. Modern freshman-composition classes are designed to help more than just the budding English major, as many of my deleted examples attempted to show.

I've taught Freshman writing for nearly 30 years, have half that number of years as a practicing journalist, and have ghost written memoirs, and edited scores of theses and dissertations.

-

I have an uncomfortable feeling that the first few pages are all rather dry, and reflect what an old-school textbook or instructor would say (or be afraid not to say). I have a few ideas but they're not terribly well thought through yet. I'll throw them out here while my impressions are fresh and hope to get some feedback.

1. Regarding presentation, I think graphics are necessary. Maybe to start with a chart of the writing process as you/we/whoever set up the present outline see(s) it. If MediaWiki can't handle graphics then, troublesome though it may be, a switch to WikkaWiki or any other that handles graphics may be in order.

2. Also regarding presentation, as I see it the collaborative editability of wikis is being exploited nicely, but their radical hypertextuality isn't. Although a reader can click on any of the headings or subheadings, at the moment this is very much a linear-hierarchical textbook. I think we need to provide multiple entry points. For example, when I am working on a paper I have quite a few vague ideas but feel intimidated to actually start writing. I also get very tense. So a nice method for me is to get a very large sheet of paper and some colored pens and do some mind mapping. So I would like to be taken to a section on that right away, rather than have to search for a tiny mention of clustering at the bottom of a page fairly deep in. (I guess I'm conflating my argument about presentation with my preferences on approach.) Without some kind of preferred linear path, some people might get lost. But a little bit of "random access" or multiple paths might be useful, too (something beyond the random module feature).

3. The content does seem very neutral and somewhat dull. I think this is a result of a very healthy desire not to make a general textbook too quirky. But I think it might be possible to make something that can be individual while covering all the expected bases by addressing my point 2.

4. Meta-discussions like this can get lost very easily when attached to a single page. There needs to be a separate space provided, and by default a wiki doesn't do that. Could there be a "Debating the overall structure" page or something along those lines? This point has been addressed briefly on Matt's blog, too. Without explicitly encouraging and supporting that kind of debate, the only way to change overall structure is to just go ahead and do it, possibly upsetting a lot of people. Because people are reluctant to mess up already good work, there's a high possibility that whoever had the initiative to come up with some kind of structure at the beginning will end up unwittingly dictating the ultimate shape of the whole book. And it's not just a question of reticence. I think when we see a structure already in place we subconsciously assume that is the optimal structure and censor out alternatives from our own mind.

I don't know how much sense this makes, but I hope it sparks a debate soon, because I do sense that a great opportunity could be missed here without it. [RickL]

I'd like to see examples here of brainstorming and freewriting. --Mattbarton.exe 20:00, 8 December 2005 (UTC)

I see a few things that need to be addressed here. I deleted the rather archaic "writing steps" section, since that's long been discredited in the literature. The chapter also appears to need editing for tone and style to make it more consistent. Compare the language in the overview with the advice for free writing. Lots to do here:
 * Add links or reference to the research chapter.
 * Talking about mind mapping and finding topics by talking to peers
 * Burke's pentad is often used as a way to generate ideas for writing --Mattbarton.exe 20:13, 1 November 2007 (UTC)

- This is Old Word Wolf speaking. Off topic: I've tried to "log in" several times but after being told I'm in, when I get to the page I'm told I'm not.

On Topic: The planning and prewriting section is weak because it spends too much time discussing the fact that it's hard to start. Students know this. The section needs dive into ways to solve the problem and stop swimming around in the morass of experiencing the problem.

I've also deleted some references to "the author." The stated audience of this composition text is first-year college students, and I think the text should -- esp. on first references -- reinforce this connection. In this spirit, I deleted from this section three or four long sentences in the first graf describing an author's query letter to a publisher. Wrong audience. Apologies to the original writer; no offense intended.

More later. m.j. tarnowski __________ [[Media:Example.ogg]]

Outline
Let me try to sum up the outline as it currently stands, to help structuring the page.

 * Overview of Planning and Prewriting
 * Finding a Topic
 * Discovering Ideas (Generating ideas?)
 * Brainstorming
 * Postpone criticism
 * Clustering
 * Freewriting
 * Welcome petty mistakes
 * Dealing with Writing Anxiety
 * Determining Your Audience
 * Developing an Outline

The outline is structured not as the page is but as the topics covered are structured, or so I tried. A futher detail can be added, picking the points from the body text. --Dan Polansky (talk) 10:30, 14 August 2008 (UTC)

Links
Two links aren't working: Tips for getting started on a paper Fighting Writer's Block
 * Outline

Matt's Thoughts on This Section
Just reading over the overview part, I was reminded of the book They Say, I Say by Graff, Birkenstein, and Durst. They talk a lot about how students struggle because they don't see scholarship as a big conversation they can take part in. Instead they think in terms of originality or personal opinions about a "hot-button" issue. I'd like to see this chapter advising students to see their essays in a context of other works of scholarship; as a contribution to an existing discourse. If a student becomes aware of a discourse and its points of contention, finding a topic becomes much easier. Furthermore, it makes it easier to select sources, tone, style, and so on.

I'd be okay with losing the "generating ideas" section altogether. I don't know any professional writers who use brainstorming, clustering, or freewriting. Again, the problem of finding a topic goes away once a student becomes aware of a discourse and isn't writing in a vacuum. --Mattbarton.exe (talk) 22:00, 13 January 2011 (UTC)

Matt H's thoughts
“''A relatively new way to get feedback is through the Internet. Numerous discussion boards, forums and blog sites provide an opportunity to compose a sentence, paragraph or even longer "draft" about your ideas''.” – Some hyperlinked examples of such sites would be helpful.

“Without a concrete plan, writers may find themselves repeating information, referring the reader to nonexistent passages, or begin stating incomplete passages to a hopelessly confused reader.” – To achieve present participle consistency (if I said that correctly), shouldn’t it be, “… or beginning to state [write?] incomplete passages to a hopelessly confused reader”? Come to think of it, if I understand the aforementioned sentence correctly, it might be clearer to say, “… or offering incomplete passages that confuse the reader.”

“Fortunately, there are sound strategies that can help to solve these problems.” – “to” can be omitted.

“The discussion will begin with some prewriting strategies that can help you discover the best topics for your papers.” – I think it would sound better to say either “This discussion …” or even “This section …”

“''Next, some strategies will be given to help you reduce writer's block or writing anxiety. Finally, you will be given tips on how to best plan your draft and reduce the likelihood of composing confusing or incoherent documents''.” – I am not vehemently opposed to passive voice, but I think it deflates the effectiveness of the above two sentences. What do you think about writing this entry at least partly in first person?

“Keeping these questions in mind while you are writing will help you to develop and produce your ideas efficiently in a limited period of time.” – I prefer, “While you are writing, keeping these questions in mind will help you develop and produce [is there a better word?] your ideas quickly and efficiently."

This wiki book was written mostly by students, correct? Regarding the general tone, would it be acceptable, then, for the tone to be inconsistent among the different sections? Additionally, will this book, or has it already been, promoted as the work of students, and if so, what are the potential pros and cons of virtually publishing a book that many may disregard because of the perceived amateur status of its authors?

“''Developing an outline, such as the examples below, can be helpful because you can keep an overview of what you want to say, check whether you have covered everything, and find what is out of scope and should be excluded. The outline can grow during the process of writing the body text as you extend it with new points coming to mind during the process.” – “Developing an outline, such as the examples below, can be helpful because'' …”

This feels grammatically incorrect. How about this instead:

“''Outlines allow you to create, and reference, an overview of what you want to say, check whether you have covered everything, and determine what is out of scope and should therefore be excluded. The outline can grow during the process of writing the body text as you extend it with new points coming to mind during the process'' [I think this last sentence needs rewording]. Below are two examples of simple and effective outlines:”

--Matt.helm (discuss • contribs) 00:56, 27 January 2011 (UTC)

Emily's Thoughts
I agree that this section does not offer what students really want to hear when writing. Dr. Barton's suggestion to replace this section with a more proactive stance regarding contributions to the academic community would be extremely beneficial for anyone to hear.

If this section should stay put, I would suggest condensing it. Speaking from a personal standpoint, when reading text on a computer I tend to read the first screen. Anything I must scroll to I end up skimming. If the ideas in this sections stay, could they be briefly mentioned with links elsewhere if students want more information? For example, the section could give a brief intro with a list of "Prewriting Tips" that would link to more specific examples? --Emily.isackson (discuss • contribs) 20:21, 27 January 2011 (UTC)

Karl's Thoughts
As per the meeting with Dr. Barton on Feb 2nd, during the semester for my part of the assignment, among other things, I will change the following: Convert topic headings into questions. Reorder the table of contents. Compress certain sections that seem overly long/verbose.

What strikes me most with this wiki is that much of it remains as two dimensional as any traditional hardbound paper text. This approach fails to take advantage of the multi dimensionality of web documentts with in-text links. The advantage of this approach would more empower the reader to get what they need most, when they need it, and without the traditional constraints of a hardbound text's ROM format. On the other hand, if a section is too generalized, web links could provide additional information.


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title: Category:User css


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Talk:Rhetoric and Composition/Writing Applications

How about "Types of Writing" as an alternative title for this? "Writing Applications" isn't entirely transparent to me; it could mean software to help with writing.

What is the deal with the so very current-traditional method of organization here? Can't we get past E(xposition)D(escription)N(arration)A(rgument), as Sharon Crowley deconstructed it over a decade ago in The Methodical Memory?

By all means. This is a wikibook! If you want to make changes, go for it. --Mattbarton.exe 17:59, 10 February 2006 (UTC)


text:
The Mojavi 3 Book/What Is Mojavi?

What Is Mojavi ?
Mojavi is a PHP framework using the Model-View-Controller (MVC) design pattern. Mojavi was created by Sean Kerr.

title: The Mojavi 3 Book/What Is Mojavi?


text:
The Mojavi 3 Book/Mojavi Features

Mojavi Features
What Mojavi provides are
 * basic framework for a flexible PHP application
 * database connectivity
 * session management
 * security handling

title: The Mojavi 3 Book/Mojavi Features


text:
The Mojavi 3 Book/Downloading Mojavi

Downloading Mojavi
You can get the Mojavi code by downloading the package at. Mojavi 3 works only with PHP 5, both in Linux or Windows. Also it is a good idea to download the API documentation.

After downloading the package, download it to some location. The package consists of

title: The Mojavi 3 Book/Downloading Mojavi


text:
The Mojavi 3 Book/Tutorials/Decorator Profiling

Prerequisites
Before reading this tutorial, one should introduce themself to the ((Global Templating - The Decorator Pattern Tutorial)(Tutorials)). Before reading this tutorial, one should introduce themself to the ((http://wiki.mojavi.org:81/159.html)(Global Templating Tutorial)).

++ Profiling

++ Profiling

Decorator profiling is a simple idea: Separate your different arrangements of Decorator template, and populators, into scripts that make those calls automatically. Decorator profiling is a simple idea: Separate your different arrangements of Decorator template, and populators, into scripts that make those calls automatically. To begin, let us take a look, evolutionarily, how one might separate the different display modes, or profiles, from the actual views.

++ Stage 1: Hardcode

In this example, a simple example of direct decoration of templates, does it's job. But it fails to provide a simple means for replicating this pattern of decorator/slot population in other Views without a copy/paste. // 1 ka ans kya h?

=Example 1: Hardcoded decorator information=

++ Step 2: Include

The second stage of abstraction is to create a separate script (a separate php file) and directly include it into your Views - eliminating copied code.

=Example 2: Included decorator information=

As you can see, all the decorator calls have been removed, and an include place in their stead. The include file is below:

=Example Profile: Default.profile.php=

++ Step 3: =setProfile=

The last stage, or what I would propose, is to create a simple method that loads our profiles for us, and perhaps provides with a few other utility functions such as

=Example 3: Included decorator information=

++ The =setProfile= Method

Don't be deceived, the =setProfile= method and the include method are, in the end, equivalent. One requires one more function call than the other, but I believe that the simplicity of the =setProfile= makes it superior, along with providing automatic detection of profiles, and automatically searching in the proper directories (The directories that would store profiles, I suppose, would be MO_TEMPLATE_DIR/templates/profiles/).

=Example 4: The setProfile method=

The member variable =$profile= will allow for a check to be run during View's preRenderCheck


text:
The Mojavi 3 Book/Tutorials/Users And Security

A brief overview
A little back ground is necessary to understand how to put a security system together. First there is the User class. It represents a visitor on a website Click here is for the User overview. You have SecurityUser classes that extend the User class. You can use this class to set and test the credentials of a visitor. In the Action class there is getCredential method that is used by a SecurityFilter to compare the required credentials of an action to the credentials of a visitor.

Credentials
Credentials can take on any form necessary to fit the needs of a particular website. It could be as simple as having only defined VISITOR and ADMIN creditials or a full blown CMS with users, roles and groups. A credential can be any legal php data type. This means it could be a STRING, an INTEGER, an ARRAY or an OBJECT. Figuring out the specifics of your credential is part of the planning you need to do for the specific site. I will show you both extremes.

The first step in using the security system is to authenticate the visitor. This is usually done through a login form that looks in a database to find a visitor to see if they have registered and have permission to be authenticated in the system. The next step is to set the credentials for the visitor. This can also be loaded from a database. This has your visitor ready to use the website to the fullest potential.

Each action, should be set with the allowed credentials for that action. You can also set up an action to not need any checking for credentials using the isSecure method.


text:
The Mojavi 3 Book/Core Components/User

The User is an object to represent a visitor in a website using the Mojavi system. Each unqiue visit to the website is represented by a separate instance of the User class and that object is persistant for the life of that visitor's session. This is a great advantange in the Mojavi system in that you can maintain information pertaining to that session in an organized and logical way.

The User object is special in that is uses a Storage object to obtain data persistence. Because of this, you can store data specific to that visitor. You can do this by making a call to the User method setAttribute and store the data there. This could be information about the user, such as their name, address or occupation. Or it would be information specific to that session, such as storing data from a multipage form. At any point during that visitor's session you can retrieve that same data by calling getAttribute.

The User can also be used to set up security for the website. Using a SecurityUser class, you can check the credentials of a visitor to see if they have permissions to be in restricted sections of the website.

In the User class you also have parameters that you can set to initialize custom implementations of the User class.

title: The Mojavi 3 Book/Core Components/User


text:
The Mojavi 3 Book/Migrating From Mojavi 2

Prerequisites
You should have a decent grasp of Mojavi2 and PHP5 before trying to upgrade to Mojavi3.

If you want a quick crash course of Mojavi 3, see Creating Your First Module.

First Things First
Before you begin transferring your applications over from Mojavi2, make sure whatever host you're using supports PHP5. You can figure out if your host supports PHP5 by running

phpinfo;

Furthermore, you need to download and install the Mojavi3 package, which can be attained by going to this location.

The Context
Probably the most important new and powerful aspect of Mojavi3 is the Context object. Once I figured out what this thing did, I fell in love with it. Basically, it is a sort of catalyst/storage object that allows you to access:
 * The $request object via getRequest
 * The $controller object via getController
 * The $user object via getUser
 * The Current Action/Module names via getModuleName and getActionName
 * And finally the Current module's directory

More or less, most classes that are exposed to the user/developer (you) are going to have a getContext function, which will allow you to access this object. And with the recent addition of cascading calls, you can perform operations that you were unable to in php4, for example:

The Old Way:

$obj       =& $request->getAttribute('myobj'); $anotherobj =& $obj->doSomethingSpecial; $anotherobj -> execute;

The New Way:

$this->getContext->getRequest->getAttribute('myobj')->doSomethingSpecial->execute;

Okay, so maybe that wasn't the best example, as it is rather lengthy, but you get my point, 1 line vs 3 lines, and no possible mistakes when dealing with large objects like copying them over without references, etc.

This subsection is to be continued....

Translating your Renderer
Mojavi2 used 'renderers' to translate the API of one templating system into a generic API that would easily allow a developer to switch out one templating system for another. For example, the Smarty templating engine uses $smarty->assign to allow you to set a variable, while patTemplate, another templating system, uses $pat->addVar. In Mojavi 2, you would then write or use an existing renderer, which you would then invoke to display your output.

Note: This was done typically through a filter, which would create the renderer object, then assign it to your $request via

$request->setAttribute('MyRenderer',$rendererObj))

Mojavi3 uses largely the same methodology, but instead of getting the renderer directly from the $request object within each of your views, it simply extends the View class.

For example:

abstract class SmartyView extends View { ..... function __construct {   $this->engine = $this->getContext->getRequest->getAttribute('MySmartyObj'); }, $value) {   $this->engine->assign($name, $value); } ..... }

Note: the use of

$this->engine = $this->getContext->getRequest->getAttribute('MySmartyObj');

was simply the best solution I could come up with for getting any object from within the view, you could also have done the following just as easily:

$this->engine = new Smarty;

View
The Mojavi3 View is mostly an abstract class, which provides a skeleton of functions to work with, thus providing the unified API as was achieved in Mojavi2 (It's unified because you are forced to comply with the naming conventions implemented by the abstract class View.)

Now, instead of initializing your Renderer object (as you would in Mojavi2) you simply extend View, and initialize that. Like shown above:

abstract class SmartyView extends View { ...

is what our new View would look like. To put this new View type into action, we extend it when declaring views for our modules. For example:

class DoSomeActionSuccessView extends SmartyView { ... }

As you can see, this is much more fluid than pulling the renderer out of $request with every new View, it's also a lot less code that you have to copy and paste, and thus less code to maintain. You may also have noticed that the naming scheme is different for the Views, instead of naming the file DoSomeActionView_success.class.php you would now name it DoSomeActionSuccessView.class.php, and name the class likewise(In Mojavi2 we just named our view classes DoSomeActionView, in Mojavi3 it's DoSomeActionSuccessView replacing 'Success' with your application's state).

This subsection is to be continued....

Actions
Actions in Mojavi3 are fairly similar to those of Mojavi2, with a few enhancement and semantic tweaks here and there. Listed Below:
 * When returning a VIEW_SUCCESS in Mojavi2, now return the View class constant corresponding to your application state, i.e.: View::Success, or View::Error
 * When checking for view types supporting execution (getRequestMethods) instead of returning REQ_POST etc., return Request::Post etc.
 * There is a new return type for getRequestMethods, Request::All, which serves all request methods.
 * The root Action class which all your actions extend now has a getContext method, which allows you access to the context object.

Configuration
Mojavi3 configurations are done, by default, using .ini files. This simple and straightforward configuration makes configuring mojavi very easy. The base syntax of these ini files is as follows:

[SECTION] ; a comment..... ConfigKey          = "%MO_APP_DIR%/my/config/value"

Because some people might not like ini files, Mojavi3 was created in such a way that you could write your own configuration handlers. For example, if you wanted to use xml files to configure your mojavi, you could write a configuration handler, plug it in, and start using your custom configuration styles.

This subsection is to be continued....


text:
The Mojavi 3 Book/Tutorials/Global Templating - The Decorator Pattern

Ever since Mojavi 3 was released earlier this year, people have been looking to create a flexible global templating solution. From using post filters to page controllers, people have been looking for a way to create simple and manageable global templates that will allow for a great deal of flexibility without compromising the need for larges amount of duplicated code.

++ Enter Decorator

The Decorator design pattern, like every other pattern, is nothing more than a way to talk about a reusable concept, or pattern, that a programmer might encounter while coding applications. The Decorator pattern's strength is it's ability to serve as a wrapper for that particular object, while leaving objects like it intact.

The Decorator pattern has been implemented in the =View= class, providing a number of new methods:

Now a brief explanation of what each of these do:

Note: these functions are in View, so all derivates of View (i.e. PHPView) have access.
 * =setSlot= - Creates a slot entry based upon the results of a specially controlled controller->forward
 * =setDecoratorTemplate= - Sets the template that you're going to use for your decorator. This method also automatically turns the decorator switch to =true=
 * =isDecorator= - returns true is setDecoratorTemplate has been called, otherwise false.
 * =getSlots= - Returns an array of the slots.
 * =getDecoratorTemplate= - Returns the decorator template.
 * =getDecoratorDirectory= - Returns the decorator directory.
 * =decorate= - A method that must be implemented in derivate Views.

++ Insert Here: Slots

Slots is a new name for an old concept. More or less, slots serve as placeholders that can be populated by the results of a =$controller->forward($mod, $act)= call. And, as you can see, the =setSlot= method takes three parameters:

The first parameter, $attributeName, serves as the name of the slot. The next two parameters will be used to get the results of that Action, put it in a buffer, and place it into the internal =$slots= member variable.

++ Let's Decorate!

The usage pattern of Views changes little with the implementation of the decorator pattern at the module level (though secondary View authors, i.e. SmartyView et al., do have a few things to play with).

Now let's look at what you're going to need to do implement the new, and NEW decorator features of Mojavi.

+++ Creating a Global Template

First off, we're going to need a great big christma..ehh..template to decorate. While I won't get into breaking down and factoring our global template, keep in mind that this is not the only way to do this. =Example 2: The Christmas Tree (myGlobalTemplate.php)=

+++ Putting the ornaments up So now that we have our decorator template, we need to decorate it. The decorating process is fairly simple, and consists of the following simple steps:
 * Setting the decorator directory using =setDecoratorDirectory= (Optional)
 * Setting the decorator template using =setDecoratorTemplate=
 * Setting slots =setSlot=

For example, =Example 3: In the View (IndexSuccessView.class.php)=

Now you might be wondering where the =content= slot is being populated. Well, =content= is a reserved slot that is automatically populated with the output of the originally requested Action/View pair. /To be Continued..../


text:
Talk:Excel VBA

Hello World
Great idea - however - you jump right in without giving newcomers any context. A new section needs to be added at the top, telling us exactly what buttons to press and options to choose to get our first program running. A "Hello World" example, in other words :-)

Recipes Wanted
Good start. Of course the information I want isn't there :-) Would it be worthwhile adding a list of recipes wanted here?  Well I'll add one anyway; formatted as a definition list.  Anyone who has a better idea is, of course, free to fix it.  --kwhitefoot 10:08, 26 September 2005 (UTC)

 * Resize Range: I need a routine that will resize a range by inserting or deleting rows as necessary. I have a template sheet that includes named ranges. I need to resize them, moving all the rows that are below up or down as necessary. --kwhitefoot 10:08, 26 September 2005 (UTC)

Protect/unprotect; if certain cells un empty or null
---Excellent work!--- I need to protect certain cells depending on a condition. Input is allowed in either column G9,H9,I9,J9,K9 and rest all cell must be protect. For example if user has input in G9 column then H9,I9,J9,K9 must be protect; same is with rest columns. Any single column used for input. How can i achieve this task.

Comparing values in 2 columns in excel
I would like to write (or insert) a program what will sequentially compare a value in cell b1 to all cells in column A. I want this to repeat for the value in b2, and so on until all values in column B have been compared to all values in column A.  If a value in column b=value in column a, then I want the program to return a "1" in that row of column C. How do I do this?

LibreOffice
Suggest create a "translation" to the free suite LibreOffice. --Diamondland (discuss • contribs) 08:27, 12 June 2012 (UTC)

Breaking into subpages
I object to breaking this book into subpages. --Dan Polansky (discuss • contribs) 10:20, 23 June 2013 (UTC)

Book name
I have renamed the book from Microsoft Excel Programming Recipes to Excel VBA. The book was only about VBA; for C++, there were just two links and no other info. "Microsoft" is unneeded in the book name. "Recipes" was okay but not strictly needed; removing it makes the book title nicely short and focused. --Dan Polansky (discuss • contribs) 07:25, 13 July 2013 (UTC)

title: Talk:Excel VBA


text: User talk:70.97.77.82

title: User talk:70.97.77.82


text:
Wikibooks:Templates/Files

The file namespace list all files uploaded to Wikibooks and describes them. Wikibooks requires that all uploaded files include proper copyright and licensing information on their description page. Some files (like images, videos, and audio files) can also be embedded on pages.

 * My file is missing a copyright template, or has . : The solution is go to the file's description page (for images, just click the image itself on the page you added it to), then edit that description page and add the correct tag(s).

Copyright information
All uploads to Wikibooks must have an template and, if not sourced under a compatible license, a  template on their file description pages, which can be added when a file is uploaded, following the examples shown below. Select the type of non-free use file from the upload form's drop-down menu. Below are examples of the possible templates the menu will add. These can be added manually afterwards if you forget to select one of them when uploading.

title: Wikibooks:Templates/Files


text:
Talk:Movie Making Manual/Cameras and formats

I'm "umming" and "erring" a bit about this section. I'm happy with the way the table of cameras links to the table of contents, although using anchors would be nice. I'm thinking about setting up links from the table of cameras to separate pages for each camera.

To do:
 * Anchors
 * Investigate automated ways to duplicate the info from the table of cameras to the camera pages

- Dan AKA Jack 12:50 Mon 26th Sept


text:
Talk:Climate Change/Mitigation Strategies/Carbon Sinks

(I have trouble understanding this information. Is Limestone carbon dioxide?  If so, would the following arrangement of words better convey the information?)

 * Limestone is one form of carbon sink as it consists largly of carbon dioxide and calcium. Limestone is generated as the ocean organisms generated their microscopic shells, which eventually collect on the ocean bottom and are pressed into the rock-like substance.

(If the foregoing is true, then some explanation is needed here as to how removal of carbon dioxide and calcium from sea water causes the following to occur. Does more carbon dioxide content require more calcium content?  Does less oxygen content require more calcium?)

As the ocean get more carbon dioxide mixed in it, rather than oxygen, then it tends to re-dissolve the limestone back into carbon dioxide and dissolved calcium.

 * Soil humus and peat is another form of carbon sink. Though it has been noted that in some types of warmer climate conditions soil humus is broken down faster than it forms.


text:
Template:Blocked

You cannot edit due to . You may appeal this action with a reasonable argument by adding the text below.

title: Template:Blocked


text: Template:Blanking

title: Template:Blanking


text: Template:User pl

title: Template:User pl


text:
Category:User pl

de:Kategorie:User pl eo:kategorio:uzanto pl it:Categoria:Utenti pl ja:Category:User pl

title: Category:User pl


text: Template:User opera

title: Template:User opera


text:
Category:Opera users

Add to your user page to add the above userbox and place yourself in this category.

title: Category:Opera users


text:
Croatian/Main Contents/Nouns

Cases
Croatian language has 7 cases: nominativ, genitiv, dativ, akuzativ, vokativ, lokativ, instrumental.

e.g. mačka (cat)

Nominative: mačka

Genitive : mačke

Dativ : mački

Akuzativ : mačku

Vokativ : mačko

Lokativ : (o) mački

Instrumental : (s) mačkom

More About Cases
Nominative: The subject of a clause is in the nominative.

Genitive: The genitive expresses possession. This case is also used after certain prepositions.

Dative: Indirect objects take the dative. The dative is also used in certain other expressions.

Accusative: The direct object of a clause is put into the accusative. Also, the objects of certain prepositions take the accusative. Verbs of motion take the accusative.

Vocative: The vocative is sometimes used when addressing people directly.

Locative: The locative indicates location, and is used to describe position with such prepositions as na and u.

Instrumental: The instrumental is used with prepostions s (with).

<–– Back to contents page

title: Croatian/Main Contents/Nouns


text: User talk:81.178.144.228

title: User talk:81.178.144.228


text:
Rueda de Casino/El Pozo

During Para el Medio, you start to 'scoop' with your left arm as you go into the middle, and lift your arm over your head as you come out.

A variant is El Pozo Con Ducha (The well, with a shower), where the hand that comes over your head wriggles to emulate a shower.

title: Rueda de Casino/El Pozo


text:
Japanese/Q&A

Feel free to post any questions you have while learning or encountering Japanese.

Post Questions Below This Line

title: Japanese/Q&A


text:
Vedic Mathematics

This book is aimed at those who want to improve their numeracy and arithmetic skills. It presents a wide range of techniques to simplify numerical calculations (to the point where many can be performed mentally without writing down any working). As well as describing these techniques, this book promotes a different way of approaching arithmetic problems than the traditional one taught in most schools. Specifically, the book promotes the idea that it is better to learn a wide range of techniques to solve a problem, (each technique optimised for a particular problem type), rather than learn just one general purpose technique to solve all problems in a particular class. Learning multiple techniques may initially seem like more work, but it will be seen that most of these techniques are very simple, making many seemingly difficult problems much easier to solve (by taking advantage of specific properties that are not present in the general case). Perhaps even more important than the more efficient arithmetic techniques is the deeper understanding gained by being aware of multiple approaches to the solution of any particular problem.

Table of Contents

 * 1) /What is Vedic Mathematics?/
 * 2) /Sutras/
 * 3) /Techniques/
 * 4) /Why Does It Work?/
 * 5) /Useful links/

Authors & Contributors
The following people have contributed significantly to this book. If you have made a significant contribution to this book, (i.e. adding significant content or extensive editing) feel free to add a reference to yourself below.

title: Vedic Mathematics


text:
Norwegian/Months and Weekdays

The names of the months in Norwegian are rather similar to those in English, because both languages have taken the names from Latin. In Norwegian, however, the names of the months do not begin with a capital letter, except when the name comes first in a sentence (as it is for all words).

The days of the week in Norwegian are as follows, and like the names of the months, do not begin with a capital letter:

title: Norwegian/Months and Weekdays


text:
Vedic Mathematics/What is Vedic Mathematics?

Welcome to the wonderful world of "Vedic" mathematics, a science that its founder claims was lost due to the advent of modern mathematics. Vedic mathematics is said by its founder to be a gift given to this world by the ancient sages of India, though there is no historical evidence whatsoever for this claim. It is a system for limited arithmetic and polynomial calculation which is simpler and more enjoyable than the equivalent algorithms of modern mathematics.

Vedic Mathematics is the name given to a supposedly ancient system of calculation which was "rediscovered" from the Vedas between 1911 and 1918 by Sri Bharati Krishna Tirthaji Maharaj (1884-1960). According to Tirthaji, all of Vedic mathematics is based on sixteen Sutras, or word-formulae. For example, "Vertically and Crosswise" is one of these Sutras. These formulae are intended to describe the way the mind naturally works, and are therefore supposed to be a great help in directing the student to the appropriate method of solution. None of these sutras has ever been found in Vedic literature, nor are its methods consistent with known mathematical knowledge from the Vedic era.

Perhaps the most striking feature of the Tirthaji system is its coherence. The whole system is interrelated and unified: the general multiplication method, for example, is easily reversed to allow one-line divisions, and the simple squaring method can be reversed to give one-line square roots. And, these are all easily understood. This unifying quality is very satisfying, it makes arithmetic easy and enjoyable, and it encourages innovation.

Difficult arithmetic problems and huge sums can often be solved immediately by Tirthaji's methods. These striking and beautiful methods are a part of a system of arithmetic which Tirthaji claims to be far more methodical than the modern system. "Vedic" Mathematics is said to manifest the coherent and unified structure of arithmetic, and its methods are complementary, direct and easy.

The simplicity of the Tirathji system means that calculations can be carried out mentally, though the methods can also be written down. There are many advantages in using a flexible, mental system. Pupils can invent their own methods; they are not limited to one method. This leads to more creative, interested and intelligent pupils.

Interest in the Tirathji's system is growing in education, where mathematics teachers are looking for something better and finding the Vedic system is the answer. Research is being carried out in many areas including the effects learning the Tirathji system has on children; developing new, powerful but easy applications of these Sutras in arithmetic and algebra.

The effectiveness of the Tirathji system cannot be fully appreciated without practising the system. One can then see why its enthusiasts claim that it is the most refined and efficient calculating system known.

"Vedic Mathematics" refers to a technique of calculation based on a set of 16 Sutras, or aphorisms, as algorithms and their upa-sutras or corollaries derived from these Sutras. Its enthusiasts advance the claim that any mathematical problem can be solved mentally with these sutras.


text:
Vedic Mathematics/Sutras

The Sixteen Sutras and their Corollaries are as follows:

/Ekadhikina Purvena/ - By one more than the previous one (Corollary: Anurupyena)

/Nikhilam Navatashcaramam Dashatah/ - All from 9 and the last from 10 (Corollary: Sisyate Sesasamjnah)

/Urdhva-Tiryagbyham/ - Vertically and crosswise (Corollary: Adyamadyenantyamantyena)

/Paraavartya Yojayet/ - Transpose and adjust (Corollary: Kevalaih Saptakam Gunyat)

/Shunyam Saamyasamuccaye/ - When the sum is the same, that sum is zero (Corollary: Vestanam)

/(Anurupye) Shunyamanyat/ - If one is in ratio, the other is zero (Corollary: Yavadunam Tavadunam)

/Sankalana-vyavakalanabhyam/ - By addition and by subtraction (Corollary: Yavadunam Tavadunikritya Varga Yojayet)

/Puranapuranabyham/ - By the completion or non-completion (Corollary: Antyayordashake'pi)

/Chalana-Kalanabyham/ - Differences and Similarities (Corollary: Antyayoreva)

/Yaavadunam/ - Whatever the extent of its deficiency (Corollary: Samuccayagunitah)

/Vyashtisamanstih/ - Part and Whole (Corollary: Lopanasthapanabhyam)

/Shesanyankena Charamena/ - The remainders by the last digit (Corollary: Vilokanam)

/Sopaantyadvayamantyam/ - The ultimate and twice the penultimate (Corollary: Gunitasamuccayah Samuccayagunitah)

/Ekanyunena Purvena/ - By one less than the previous one (Corollary: Dhvajanka)

/Gunitasamuchyah/ - The product of the sum is equal to the sum of the product (Corollary: Dwandwa Yoga)

/Gunakasamuchyah/ - The factors of the sum is equal to the sum of the factors (Corollary: Adyam Antyam Madhyam)

title: Vedic Mathematics/Sutras


text:
How to Pass a Course/Practice

The old adage says practice makes perfect. That´s true of everything in life, so too for a student. Too often it happens that we study hard for some time, attain a peak level of mastery and feel we have attained it once and for all. Then we stop practicing confident that we have it. Sadly that´s not true for anything. Things have a tendency of slipping away if you don't practice. So practice, revise in case of changes in theory. Keep solving repeatedly in case of problems.

Once we have practiced something a sufficient number of times, it seems that our bodies remember the correct responses much better than our minds do. This is what makes us able to, for example, drive a car and carry on a conversation at the same time.

title: How to Pass a Course/Practice