text:
Educational Technology Innovation and Impact/Multimedia Courseware/Electronic Paper

Electronic paper, e-paper is a technology that let the text on a piece of paper to be re-written. The paper is actually made of organic electronics that use conductive plastic which restrain tiny balls that react to an electric charge, changing the page in much the same way that pixels change on a computer monitor.

Electronic paper was developed in order to overcome some of the limitations of computer monitors. For example, the backlighting of monitors is hard on the human eye, whereas electronic paper reflects light just like normal paper. It is easier to read at an angle than flat screen monitors because it is made of plastic, electronic paper has the potential to be flexible. It is light and potentially inexpensive.

Books with printed pages are unique in that they embody the simultaneous, high-resolution display of hundreds of pages of information. The representation of information on a large number of physical pages, which may be physically turned and written on, constitutes a highly preferred means of information interaction. An obvious disadvantage of the printed page, however, is its immutability once typeset. We are currently developing electronically addressable paper-page displays that use real paper substrates. This effort includes the development of novel electronically addressable Contrast media, microencapsulation chemistry, and desktop printing technologies to print functional circuits, logic, and display elements on paper or paper-like substrates, including interconnecting vias and multi-layer logic.


text:
Educational Technology Innovation and Impact/Virtual Learning Environments/Virtual Classroom

Virtual classroom

“Virtual classroom it is an environment unlike the traditional classroom. In actual fact, the virtual classroom is wherever you and your computer happen to be. It could be in your room, in one of the University microcomputer labs, or at an isolated site far removed from the KSU campus. Your virtual class schedule is whatever time you want it to be” Virtual classroom provides a perfect environment for online training and gives a feel of being in the classroom itself. Virtual classroom integrates the best learning practices with the power of internet to provide a dynamic learning platform to the learner. The virtual classroom/e-learning has innumerable advantages and the most vital of which are the saving of time and cost, no interaction between teachers and students and no sense of peer pressure.

Of course, taking internet-based course at the pre-College/university level can have both pros and cons. Below will follow some of them that would make you decide if virtual learning is for you.

Positive aspects of virtual classroom/e-learning.

“Independence and time Management

Students who take courses online often sharpen their ability to work on their own, and they also expand experience in managing their time efficiently. With nobody to stand over them and make them work, virtual learners tend to develop these skills more rapidly than if they were to learn strictly in a traditional classroom.

Advanced and specialized classes

In many cases, small school and rural schools simply cannot offer advanced or specialized classes. Virtual education gives students the opportunity to gain experience in areas that would otherwise remain out of reach.

Emphasis on the written work

Strong writing skills are essential to success in secondary and higher education as well as in the workplace. Virtual learning/distance education teaches students to communicate more effectively through writing, because the questions they ask and the work they complete is based almost solely on the written word. Virtual learning clearly gives students the chance to widen writing skills.

Knotty aspects of virtual/distance education

Lack of face-to face interaction

Some educators dispute that both teacher-student and student-student contact are essential to the learning process, and online classes eradicate these elements of education altogether. Also, students who excel at class participation need to deem that this piece of the learning puzzle will be missing as well.

The need to self-start

Virtual education actually lets students make their own schedules. Those who have a hard time with self-motivation will undoubtedly have problem in this type of educational setting”

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


text:
Educational Technology Innovation and Impact/Assistive Technology/Screen Readers

A screen reader is a software application that attempts to identify and interpret what is being displayed on the screen. This is then presented to a blind user as speech (by text-to-speech) or by driving a Braille display. Screen readers are used by people with little or no functional vision: people with some vision often use screen magnifiers” Besides people with low-vision, people with limited-vision, learning disabilities, mobility impairments, English as a second language, the elderly, and people with reading delays can use text-to-speech technology as an assistive technology.

Screen readers (or speech output systems) are designed to aid blind people give them access to standard computers and software such as word processors, spreadsheets, email, icons, windows and internet browsers. Screen reader have gave people with low vision a very great opportunity to access wide range of information, neuro-processing and the communication ideas that was behind their reach. “However, using a screen reader is, according to some users, considerably more difficult than using Graphical User Interface and many applications have specific problems resulting from the nature of the application (e.g. animations in Macromedia Flash) or failure to comply with accessibility standards for the platform (e.g. Microsoft word and Active Accessibility”

A standard computer whether is laptop or desktop can be personalized by tallying a screen reader, which enable the computer to speak. The screen reader let navigation around the computer screen and presents what is happening on the screen to the user in a significant way using speech output. The computer is used by mingling a standard keyboard and keyboard shortcuts rather than a mouse use the computer.

There are various types of screen readers available and some are more popular in different environments. Some more sophisticated products are designed to work best in an education or employment situation as they can be configured to work with different programs. Others are more for home use as they may offer restricted features in comparison with more expensive screen readers, focusing on word processing, Internet and email.


text:
User talk:Rkshiwed

The Internet is copyrighted
Did you read the bottom of the edit screen? It reads:

 * You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource. DO NOT SUBMIT COPYRIGHTED WORK WITHOUT PERMISSION!

You cannot copy from most Internet web pages to Wikibooks. Even when there is no copyright notice, most Internet web pages are copyrighted – you cannot copy from them unless you have a license. We are a place for writing textbooks, not a repository of quotes. You might be able to use a few sentences under fair use, but not more than that.

It is okay to link to other web sites. Just write the URL, like this: http://www.microsoft.com ... or make a numbered link, like this: makes

Please do not copy large amounts of unlicensed text into Wikibooks. If you do this, your text will be deleted. --Kernigh 20:45, 16 April 2006 (UTC)

title: User talk:Rkshiwed


text:
General Relativity/Introduction to Tensors

In this section:
 * ../What is a tensor?/
 * ../Contravariant and Covariant Indices/
 * ../Einstein Summation Notation/
 * ../Rigorous Definition of Tensors/
 * ../Coordinate systems and the comma derivative/


text:
User:Kernigh/monobook.js

/* Top of Javascript */

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// Gets the article lemma, with the namespace and with sub pages. function global_get_tidy_title { // get the article link from the label 'ca-edit' out of the document text. var editlk = document.getElementById('ca-edit');

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title: User:Kernigh/monobook.js


text:
User:One-dimensional Tangent~enwikibooks

I'm the same person as the One-dimensional Tangent at Wikipedia.


text:
User talk:One-dimensional Tangent~enwikibooks

Note: I'm not very active on Wikibooks, so if you want to leave a message that'll get to me, you might be better of leaving it at my Wikipedia talk page. —One-dimensional Tangent 21:51, 16 April 2006 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called One-dimensional Tangent. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name One-dimensional Tangent~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:34, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:19, 19 April 2015 (UTC)


text:
Accountancy/The Trial Balance

A trial balance (OR a list of account balances) is a list of all ledger balances (which form part of the double entry system only) shown in debit and credit columns. The totals of each columns should be the same if all debits and credits are entered systematically.

The trial balance is not a financial document officially, but it is just a method used to test the accuracy of the double entry bookkeeping methods. Because of this, the exact format may vary but in practice many trial balance reports appear very similar. A common format is to list the balance sheet accounts first, followed by the income statement accounts.

title: Accountancy/The Trial Balance


text: Template:Seasonality

title: Template:Seasonality


text: Template:SeasonalitySpec

title: Template:SeasonalitySpec


text:
Cookbook:Nut Roll

| Dessert

This recipe is for an Eastern European dessert that goes by many various names, but is often translated as nut roll in English. This variation is a traditional Slovakian version containing walnuts.

Dough

 * 1) Dissolve the yeast in the lukewarm milk. Mix well, and lest rest until foamy.
 * 2) Stir the sugar, shortening, and salt into the yeast mixture. Let cool slightly, then mix in the eggs.
 * 3) Place half of the flour in a bowl, and gradually stir in the liquid mixture. Mix well, then knead in the remaining flour. The dough should be smooth and not sticky.
 * 4) Cover the dough, and let it rise in a warm place for about 2 hours until doubled in volume.
 * 5) Gently knead the dough to deflate it. Divide it into 6 pieces, and let it stand for 10 minutes.

Filling

 * 1) Combine all of the ingredients for the filling, and set aside until the dough is ready.

Assembly

 * 1) Roll each dough piece out, and spread with the nut filling mixture. Roll up the dough to make a spiral.
 * 2) Place the rolls on a greased and/or parchment-lined baking sheet. Let rise for 1 hour.
 * 3) Make the egg wash by beating together the eggs with a dash of evaporated milk. Brush the tops of the rolls with the egg wash.
 * 4) Bake for 35–40 minutes at 350°F (180°C) until golden and cooked through.
 * 5) Brush the hot rolls with melted butter, and let cool.

Notes, tips, and variations

 * Nut rolls freeze well for up to six months after being baked.

title: Cookbook:Nut Roll


text:
Radiation Oncology/Breast/RT toxicity

Breast Cancer RT Toxicity

 * Skin care
 * Lymphedema
 * Lung toxicity
 * Cardiac toxicity
 * Thyroid

title: Radiation Oncology/Breast/RT toxicity


text:
Talk:A-level Physics/Wave properties/Reflection and Refraction

Specification
From the OCR GCE Physics A specification. Tick with ✔ when you feel each part of the specification has been covered. Try not to add much more than what is in this list as it would not appear in the exam anyway. Use links to wikipedia for more depth in a topic.

 * 1) Recall the laws of refraction of light.
 * 2) Define refractive index n as Ci / Cr and recall the use of the expression n = sin i / sin r.
 * 3) Describe what is meant by critical angle and total internal reflection.
 * 4) Relate refractive index to critical angle by the equation n = 1 / sin C.
 * 5) Describe the application of total internal reflection to the transmition of light accross an optic fibre.
 * 6) Demonstrate an awareness of the multipath dispersion of a pulse of light in an optic fibre and how, in practice, this problem is overcome.


text:
Talk:A-level Physics/Wave properties/Waves

Specification
From the OCR GCE Physics A specification. Tick with ✔ when you feel each part of the specification has been covered. Try not to add much more than what is in this list as it would not appear in the exam anyway. Use links to wikipedia for more depth in a topic.

 * 1) Describe what is meant by wave motion as illustrated by vibrations in ropes, springs and ripple tanks.
 * 2) Appreciate that waves can be reflected and refracted.
 * 3) Understand and use the terms displacement, amplitude, period, phase difference, frequency, wavelength and speed.
 * 4) Deduce, from the definitions of speed, frequency and wavelength the equation $$ v = f * \lambda\,$$.
 * 5) Recall and use the equation $$ v = f * \lambda\,$$.
 * 6) Appreciate the energy transfer due to a progressive wave.
 * 7) Describe the nature of the motions in transverse and longitudinal waves.
 * 8) Interpret graphical representations of transverse and longitudinal waves.
 * 9) Understand polarisation as a phenomenon associated with transverse waves.
 * 10) Determine the frequency of a sound using a calibrated c.r.o.


text:
User talk:Justdig

Ju s td i  g

Justdig

title: User talk:Justdig


text:
Automobile Repair/Oil change

Performing an Oil Change

Changing your auto's oil regularly is essential to your engine's proper operation. As dirt and metal filings build up in your car's oil it becomes less able to provide proper lubrication. With time your oil will degrade, causing Viscosity to increase, further limiting its ability to lubricate the engine. This guide will not get into specifics for each model of auto, more info can be found online and in the various brands of repair manuals available.

In recent years, both the metallurgy of engines and the chemistry of oil have seen great advances, so that many engines outlast the rest of the car without need for major overhauls or rebuilding, if given proper scheduled lubrication.

Car manuals state the recommended oil service interval for the car; there are often a specification for easy duty and one for heavier duty. Contrary to what is sometimes assumed, sustained operation at higher power levels and higher temperatures constitutes easier duty, as far as the oil is concerned, as it allows any contamination of water vapor and/or fuel to boil off. Thus, engines which are mostly restricted only to short usage in the city will require more frequent oil changes due to the buildup of these contaminants. Extreme high temperatures, however, will cause normal oils first to deteriorate, then to "carbonize", i.e. turn into hard solid carbon particles, with bad effects on lubricated parts; this generally is only a problem in engines which badly overheat, or in the bearings of turbochargers which do not have mechanisms to prevent this, such as water cooling for the bearings, or systems to continue to pump the oil after engine shutoff. In these cases, in addition to more frequent oil changes, use of synthetic oil, which is more stable to high temperatures, may be of advantage.

Required

 * 1) Basic Socket set and Ratchet. Almost any basic socket set 3/8in drive will have the proper size for most cars and light trucks.
 * 2) Oil of the correct type for your auto.  Your car's manual will list the proper type and amount of oil to use.
 * 3) Oil filter. Someone at the auto parts store will help you find the correct filter for your auto. Quality of filters varies widely, in terms of quality and amount of filtration material as well as quality of such internal components as bypass valves, and much debate is documented on Usenet and the Web regarding analysis of the internal components of various brands.
 * 4) Something to catch the used oil.  I use an old kitchen pot, but car parts stores sell suitable alternatives.
 * 5) Oil filter wrench.
 * 6) The "strap type" looks a bit like a large egg frying ring with a handle, and wraps around the filter body and tightens its grip as it is twisted, somewhat similar to kitchen gadgets sold for opening tops of jars. It often has two separate settings for wide and narrow filters; however the wide range of filters used currently does not guarantee that either of these settings on a given wrench will fit, so a few sizes of this type of wrench are available. The handle may be fixed in the plane of the strap, or swivel to allow angled access in tight areas.
 * 7) The second type of wrench is the "cup" type, which fits over the end of the filter, which usually has several flutes pressed in, and in turn attaches to a socket wrench. This type of wrench comes in several sizes which must be fit to the particular filter.
 * 8) It is also possible to pierce the oil filter with a screw driver and a hammer if you do not have access to any tools.

Optional

 * 1) Ramps or jack stands. You may find it more comfortable to purchase some ramps or jack stands to raise the auto a bit off the ground while you work. Proper use of these is outside the scope of this how-to, but be sure to follow all directions and warnings.
 * 2) Cardboard. Also, I use a large piece of cardboard to keep my back out of the dirt when working under the car. It will also prevent ugly oil spills on the floor.
 * 3) Sealing ring for the drain plug. It's a good idea to replace the copper or alu sealing ring of the drain plug. Again, the auto parts store will help you.

Step 1: Removing the old oil
Firstly run the engine on idle for a few minutes, This makes the oil warm which will let it drain from the sump faster. After turning off the engine, get under the auto and locate the oil pan, usually directly under the engine. At the base of the oil pan there will be a drain plug. Position the bucket/pot/etc. you decided to use for old oil below and in front of the drain plug. Remove the drain plug with the ratchet and socket set. Allow the oil to drain completely. Replace the drain plug, preferably with a new sealing ring.

There are two schools of thought regarding draining the old oil; one believes in letting the oil drain for a long time so as to extract as much of the old, presumably dirty and contaminated oil from the oil passages as possible. The other philosophy is the opposite; to complete the entire operation in the shortest possible time, in order that there be some residual oil still present in the oil passages to provide some lubrication during the period while the oiling system (including the filter) must refill, on the grounds that, if the oil is changed on a reasonably frequent schedule, a few ounces of contaminated oil in the new oil for the next few months are preferable to a few seconds of oil starvation.

Step 2: Removing the old oil filter, and installing the new one
Locate your auto's oil filter. Position a rag below it, as some oil will come out as you unscrew it with the oil filter wrench. Unscrew the old oil filter, and put it aside. Lubricate the seal on the new oil filter with a few drops of oil. Check the old filter to ensure that the seal is still there and did not stick to the engine, as happens occasionally and is easy to miss; in such a case, the new filter will not seal correctly and chronic major oil leaks will result. Then screw it on until it starts to get tight and then just 3/4 of a turn more. This ensures the filter will be properly seated with out over-tightening it. Since a properly installed filter will become slightly more tightly sealed over time as the gasket swells somewhat, an overtightened filter can become a major problem to remove, with strap type wrenches slipping before the filter turns and cup-type filters actually breaking before the filter loosens.

Step 3: Refilling with new oil
Locate your auto's oil fill spout, generally on the top of the engine somewhere. Take the top off, and fill with the amount of oil specified in your auto's manual using a funnel to avoid spilling. Replace top. If you're like many people and don't have a manual and you were able to fill the oil filter, go ahead and fill the engine until the oil is level with the full line on the dipstick. Start the engine and let idle for a few minutes, then shutoff the engine, wait a few minutes for the oil to drain into the sump, and check the dipstick to make sure the oil is at the proper level. Always check the oil with the engine off unless the dipstick says otherwise. Do not overfill or underfill. Remember to dispose of your old engine oil correctly at your local waste recycling center.

Step 4: Remember your oil change
Note down the mileage and date of the oil change, so you know when to change it the next time. But remember that the full service is not only the oil change, but many other service steps (air filter, spark plugs, checks, ...). So don't mark the service as done and "forget" all the other steps.
 * 1) you'll often find a small paper "next oil service" near the engine
 * 2) in the service booklet - if it's not already lost (very recent cars only have an electronic service "booklet" located at the manufacturers computers)
 * 3) "modern" cars also have an electronic service reminder, which can be reset with a special dashboard button sequence and/or electronically through the OBD connector.

Done
That's it. Your auto is now ready for another thousands of miles. The change interval ranges widely from 3000 to 20000 miles (5000 - 30000 km) and largely depends on the cars make and model and the oil used. Consult your cars manual and the packaging that came with your oil to determine its proper use. However, "long life" intervals above ~10000 miles (~15000 km) are usually not recommended for cars often used in short ranges.

title: Automobile Repair/Oil change


text:
Gerris Manual/Object hierarchy

 * GfsSimulation
 * GfsOcean
 * GfsAdvection
 * GfsPoisson

 * GfsVariable
 * GfsVariableTracer
 * GfsVariableResidual
 * GfsVariableFiltered
 * GfsVariableCurvature

 * GfssurfaceBc

 * GfsBox
 * GfsBoxNotAdapt
 * GfsGedge

 * GfsBcDirichlet
 * GfsBcNeumann
 * GfsBcFlather

 * GfsBoundary
 * GfsBoundaryInflow_constant
 * GfsBoundaryOutflow
 * GfsBoundaryMpi

 * GfsRefine
 * GfsRefineSolid
 * GfsRefineSurface
 * GfsRefineDistance
 * GfsRefineHeight

 * /GfsEvent/ — Any action to be performed at a given time
 * GfsInit
 * GfsInitFlowConstant
 * GfsInitFraction
 * GfsInitVorticity
 * GfsAdapt
 * GfsAdaptVorticity
 * GfsAdaptStreamlineCurvature
 * GfsAdaptFunction
 * GfsAdaptGradient
 * GfsAdaptCurvature
 * GfsAdaptNotBox
 * GfsEventSum
 * GfsEventHarmonic
 * GfsEventStop
 * /GfsEventScript/ — Executing a shell-script at given times
 * GfsSourceGeneric
 * GfsSourceScalar
 * GfsSource
 * GfsSourceControl
 * GfsSourceDiffusion
 * GfsSourceDiffusionExplicit
 * GfsSourceVelocity
 * /GfsSourceViscosity/
 * GfsSourceFriction
 * GfsSourceCoriolis
 * GfsSourceTension
 * GfssourceHydrostatic
 * GfsRemoveDroplets
 * GfsRemovePonds
 * GfsEventFilter
 * /GfsOutput/ — Writing simulation data
 * GfsOutputTime
 * GfsOutputProgress
 * GfsOutputProjectionStats
 * GfsOutputDiffusionStats
 * GfsOutputSolidStats
 * GfsOutputAdaptStats
 * GfsOutputTiming
 * GfsOutputBalance
 * GfsOutputSolidForce
 * GfsOutputLocation
 * GfsOutputSimulation
 * GfsOutputBoundaries
 * GfsOutputParticle
 * GfsOutputScalar
 * GfsOutputScalarNorm
 * GfsOutputScalarStats
 * GfsOutputScalarSum
 * GfsOutputScalarMaxima
 * GfsOutputScalarHistogram
 * GfsOutputErrorNorm
 * GfsOutputCorrelation
 * GfsOutputSquares
 * GfsOutputStreamline
 * GfsOutputPPM

title: Gerris Manual/Object hierarchy


text:
Gerris Manual/Object hierarchy/GfsOutput

This generic object is a ../GfsEvent/ which also defines where to write the data to output.

The syntax in parameter files is as follows:

[ ../GfsEvent/ ] FILE

where FILE is either a string defining the file in which to write the output, or a shell-script enclosed within braces to which the output will be piped. Two file names have special meaning: "stderr" and "stdout" for the standard error and standard output respectively.

If a C-like formatting string appears in the file name, it is interpreted as follows:

 * %d :	is replaced with the current processor number.
 * %ld :	is replaced with the current time step number.
 * %f :	is replaced with the current physical time.

Note that most of the C language format specifiers are recognized (i.e. it is possible to use formatting strings like %05.2f etc...).

If the simulation does not start at time zero the existing files are appended otherwise they are overwritten.

The "pipe" feature of GfsOutput can for example be used to do on-the-flight post-processing of the data stream, as in the following example:

GfsOutputPPM { istep = 1 } { ppmtoy4m -v 0 -F 24:1 | mpeg2enc -v 0 -o vorticity.mpg } { v = Vorticity }

which will convert the PPM stream generated by GfsOutputPPM directly to MPEG using the MJPEG tools collection.


text:
Gerris Manual/Object hierarchy/GfsEvent

Events are used to control any action which needs to be performed at a given time during a simulation. This includes one off actions as well as periodically repeated actions.

The syntax in parameter files is as follows:

GfsEvent { start = 0.1 istart = 10 ( step = 1.2 | istep = 10 ) end = 0.4 iend = 123 }

with:

 * start:	Physical starting time (default is zero). The "end" keyword can be used to indicate the end of the simulation.
 * istart: Time step starting time (default is zero).
 * step:	Repeat every step physical time units (default is infinity).
 * istep:	Repeat every istep time steps (default is infinity).
 * end:	Stop at or before this physical time (default is infinity).
 * iend:	Stop at or before this number of time steps (default is infinity).

title: Gerris Manual/Object hierarchy/GfsEvent


text:
Gerris Manual/Object hierarchy/GfsEventScript

GfsEventScript can be used to execute a shell-script at given intervals.

The syntax in parameter files is as follows:

[ ../GfsEvent/ ] { COMMANDS }

where COMMANDS is the script to be executed with /bin/sh.

Several shell variables are set:

 * GfsTime:	the physical time
 * GfsIter:	the iteration number
 * GfsPid:	the processor number
 * GFS_STOP:	if the exit status of the shell script is GFS_STOP the simulation is terminated


text:
Calculus/Parametric Introduction

Introduction
Parametric equations are typically defined by two equations that specify both the $$x,y$$ coordinates of a graph using a parameter. They are graphed using the parameter (usually $$t$$) to figure out both the $$x,y$$ coordinates.

$$\begin{align}x&=t\\y&=t^2\end{align}$$
 * Example 1

Note: This parametric equation is equivalent to the rectangular equation $$y=x^2$$.

$$\begin{align}x&=\cos(t)\\y&=\sin(t)\end{align}$$
 * Example 2

Note: This parametric equation is equivalent to the rectangular equation $$x^2+y^2=1$$ and the polar equation $$r=1$$.

Parametric equations can be plotted by using a $$t$$-table to show values of $$x,y$$ for each value of $$t$$. They can also be plotted by eliminating the parameter though this method removes the parameter's importance.

Forms of Parametric Equations
Parametric equations can be described in three ways:
 * Parametric form
 * Vector form
 * An equality

The first two forms are used far more often, as they allow us to find the value of the component at the given value of the parameter. The final form is used less often; it allows us to verify a solution to the equation, or find the parameter (or some constant multiple thereof).

Parametric Form
A parametric equation can be shown in parametric form by describing it with a system of equations. For instance:

$$\begin{align}x&=t\\y&=t^2-1\end{align}$$

Vector Form
Vector form can be used to describe a parametric equation in a similar manner to parametric form. In this case, a position vector is given:

$$\binom{x}{y}=\binom{t}{t^2-1}$$

Equalities
A parametric equation can also be described with a set of equalities. This is done by solving for the parameter, and equating the components. For example:

$$\begin{align}x&=t\\y&=t^2-1\end{align}$$

From here, we can solve for $$t$$ :

$$\begin{align}t&=x\\t&=\pm\sqrt{1+y}\end{align}$$

And hence equate the two right-hand sides:

$$x=\pm\sqrt{1+y}$$

Converting Parametric Equations
There are a few common place methods used to change a parametric equation to rectangular form. The first involves solving for $$t$$ in one of the two equations and then replacing the new expression for $$t$$ with the variable found in the second equation.

$$\begin{align}x&=t-3\\y&=t^3\end{align}$$
 * Example 1

$$x=t-3$$ becomes $$x+3=t$$

$$y=(x+3)^3$$

$$\begin{align}x&=3\cos(t)\\y&=4\sin(t)\end{align}$$
 * Example 2

Isolate the trigonometric functions

$$\begin{align}\cos(t)&=\frac{x}{3}\\\sin(t)&=\frac{y}{4}\end{align}$$

Use the identity

$$\begin{align}&\cos^2(t)+\sin^2(t)=1\\&\frac{x^2}{9}+\frac{y^2}{16}=1\end{align}$$

title: Calculus/Parametric Introduction


text:
Cookbook talk:Tartar Sauce

Follow-up notes
I've done some further experimenting. In the absence of pickle juice, dill weed and vinegar also work nicely (also, significantly lowering the amount of ketchup and mustard helps too). I'll try to work out the correct proportions and update the recipe if I have time. —Locke Cole • t • c 10:04, 17 April 2006 (UTC)

title: Cookbook talk:Tartar Sauce


text:
Management for IT Professionals

Topics
Topics:
 * Strategy
 * Mission
 * Core Competency
 * Focus
 * Market
 * Market Segment
 * Product
 * Service
 * Marketing
 * Quality
 * Production
 * Reengineering
 * Standards

Forward Planning
Forward planning in IT is critical if an organization's future needs are going to be met. Network design, hardware and software are constantly changing and being improved with new technologies and trends. Besides the technology, organizations change locations, the number of staff, their approach to marketing and communication and so do their customers. There are several areas to consider in forward IT planning:
 * The new ways that people will be communicating eg. VOIP, Instant Messaging and Blogs
 * The possible new locations that your organisation will be operating in
 * How many IT staff will be required and what specialties they should have
 * How desktop and laptop PCs will be upgraded over time
 * How servers will be upgraded
 * How network hardware and bandwidth will be upgraded
 * How possible acquisitions by your organisation can be accommodated
 * New applications that could be implemented on the server or client
 * New technologies such as mobile internet-aware devices or server virtualisation

Outsourcing
It may or may not be worth outsourcing IT services.

Some important factors include:
 * the cost of doing it yourself as opposed to paying someone else,
 * the burden of hiring and managing staff,
 * whether staff are available at a reasonable cost,
 * whether a company can utilise overseas people to save on labour costs
 * the potential liability in doing it yourself,
 * the accountability you can gain from service level agreements if you pay someone else to do it
 * the frequency of the task concerned - an infrequent job might not sustain a full-time person

Pretty much any area of IT can be outsourced. Areas that can be outsourced include:
 * email security such as spam and virus filtering
 * email servers
 * network security/design/management
 * this includes firewalls/routers/network links
 * software development
 * web development/design
 * desktop publishing
 * IT strategy

Policies
Policies assist both with keeping organisations and their employees accountable and with limiting the organisation's liability. Policies set the standards on what is acceptable and what is not. Policies are essential for setting out the guidelines for:
 * monitoring of employees' email, files, print jobs and phone calls. This is enforced by privacy laws, particularly in the US and Australia.
 * system administrators use of power - eg. allowing others to see someone's email or web access logs, accessing senior management's email, accessing financial information, auditing file access
 * acceptable websites and whether unacceptable ones will be blocked by a proxy server.
 * acceptable language to use when representing the company
 * personal email such as Hotmail/Yahoo and when they should be accessed if at all
 * personal emails within the organisation's email system - particularly who owns them
 * personal phone calls on both mobile/cellular phones and office phones
 * filing of emails with projects
 * how to use the company logos ie. preserving the organisation's visual identity
 * who can change the company website(s)

Procedures might also be useful for when:
 * someone wants to make a change to the company website
 * to be completed...
 * Awareness policies about the securities of official data as well as adopting new researches results which can bring more productivity at work.

Liability
There are many areas where IT affects the legal liability of an organisation. An IT professional needs to be aware of them and attempt to minimise them. Some examples are:
 * licensing - using software without being licensed could result in lawsuits
 * access control to files - sensitive government projects or information pertaining to confidentiality agreed projects will need to be carefully managed, not all staff will necessarily need access
 * record keeping standards and procedures - as a result of major corporate failures, government tax and reporting laws are becoming stricter. These spill over into IT
 * backup procedures - you may not want to keep some things because they represent a risk
 * supplier contracts - only IT will know the intimate details of suppliers contracts and will need to be aware of payment obligations, marketing the supplier may do using your name
 * tendering suppliers - potential suppliers may sue if they feel they have been discriminated against during the tender process

title: Management for IT Professionals


text:
Rock Climbing

Rock climbing is a most exciting sport that has a very rich history. This guide will take you through the basics of the sport, and help you to choose the right equipment. It also provides several training regimes designed to help you climb better, no matter what your skill level is. Plus, safety issues are also addressed.

Table of Chapters

 * /Introduction/
 * /Equipment/
 * /Technique/
 * /Bouldering/
 * /Sport Climbing/
 * /Trad Climbing/
 * /Training/
 * /Climbing Around the World/

Contributors

 * Fastesthamster

Escalade

title: Rock Climbing


text:
Cognitive Psychology and Cognitive Neuroscience/Problem Solving from an Evolutionary Perspective

Introduction
Same place, different day. Knut is sitting at his desk again, staring at a blank paper in front of him, while nervously playing with a pen in his right hand. Just a few hours left to hand in his essay and he has not written a word. All of a sudden he smashes his fist on the table and cries out: "I need a plan!"

That thing Knut is confronted with is something everyone of us encounters in his daily life. He has got a problem – and he does not really know how to solve it. But what exactly is a problem? Are there strategies to solve problems? These are just a few of the questions we want to answer in this chapter.

We begin our chapter by giving a short description of what psychologists regard as a problem. Afterwards we are going to present different approaches towards problem solving, starting with gestalt psychologists and ending with modern search strategies connected to artificial intelligence. In addition we will also consider how experts do solve problems and finally we will have a closer look at two topics: The neurophysiological background on the one hand and the question what kind of role can be assigned to evolution regarding problem solving on the other.

The most basic definition is “A problem is any given situation that differs from a desired goal”. This definition is very useful for discussing problem solving in terms of evolutionary adaptation, as it allows to understand every aspect of (human or animal) life as a problem. This includes issues like finding food in harsh winters, remembering where you left your provisions, making decisions about which way to go, learning, repeating and varying all kinds of complex movements, and so on. Though all these problems were of crucial importance during the evolutionary process that created us the way we are, they are by no means solved exclusively by humans. We find a most amazing variety of different solutions for these problems in nature (just consider, e.g., by which means a bat hunts its prey, compared to a spider). For this essay we will mainly focus on those problems that are not solved by animals or evolution, that is, all kinds of abstract problems (e.g. playing chess). Furthermore, we will not consider those situations as problems that have an obvious solution: Imagine Knut decides to take a sip of coffee from the mug next to his right hand. He does not even have to think about how to do this. This is not because the situation itself is trivial (a robot capable of recognising the mug, deciding whether it is full, then grabbing it and moving it to Knut’s mouth would be a highly complex machine) but because in the context of all possible situations it is so trivial that it no longer is a problem our consciousness needs to be bothered with. The problems we will discuss in the following all need some conscious effort, though some seem to be solved without us being able to say how exactly we got to the solution. Still we will find that often the strategies we use to solve these problems are applicable to more basic problems, too.

Non-trivial, abstract problems can be divided into two groups:

Well-defined Problems
For many abstract problems it is possible to find an algorithmic solution. We call all those problems well-defined that can be properly formalised, which comes along with the following properties:

 * The problem has a clearly defined given state. This might be the line-up of a chess game, a given formula you have to solve, or the set-up of the towers of Hanoi game (which we will discuss later).

 * There is a finite set of operators, that is, of rules you may apply to the given state. For the chess game, e.g., these would be the rules that tell you which piece you may move to which position.

 * Finally, the problem has a clear goal state: The equations is resolved to x, all discs are moved to the right stack, or the other player is in checkmate.

Not surprisingly, a problem that fulfils these requirements can be implemented algorithmically (also see convergent thinking). Therefore many well-defined problems can be very effectively solved by computers, like playing chess.

Ill-defined Problems
Though many problems can be properly formalised (sometimes only if we accept an enormous complexity) there are still others where this is not the case. Good examples for this are all kinds of tasks that involve creativity, and, generally speaking, all problems for which it is not possible to clearly define a given state and a goal state: Formalising a problem of the kind “Please paint a beautiful picture” may be impossible. Still this is a problem most people would be able to access in one way or the other, even if the result may be totally different from person to person. And while Knut might judge that picture X is gorgeous, you might completely disagree.

Nevertheless ill-defined problems often involve sub-problems that can be totally well-defined. On the other hand, many every-day problems that seem to be completely well-defined involve- when examined in detail- a big deal of creativity and ambiguities.

If we think of Knut's fairly ill-defined task of writing an essay, he will not be able to complete this task without first understanding the text he has to write about. This step is the first subgoal Knut has to solve. Interestingly, ill-defined problems often involve subproblems that are well-defined.

Restructuring – The Gestalt Approach
One dominant approach to Problem Solving originated from Gestalt psychologists in the 1920s. Their understanding of problem solving emphasises behaviour in situations requiring relatively novel means of attaining goals and suggests that problem solving involves a process called restructuring. Since this indicates a perceptual approach, two main questions have to be considered: This is what we are going to do in the following part of this section.
 * How is a problem represented in a person's mind?
 * How does solving this problem involve a reorganisation or restructuring of this representation?

How is a problem represented in the mind?
In current research internal and external representations are distinguished: The first kind is regarded as the knowledge and structure of memory, while the latter type is defined as the knowledge and structure of the environment, such like physical objects or symbols whose information can be picked up and processed by the perceptual system autonomously. On the contrary the information in internal representations has to be retrieved by cognitive processes.

Generally speaking, problem representations are models of the situation as experienced by the agent. Representing a problem means to analyse it and split it into separate components: Therefore the efficiency of Problem Solving depends on the underlying representations in a person’s mind, which usually also involves personal aspects. Analysing the problem domain according to different dimensions, i.e., changing from one representation to another, results in arriving at a new understanding of a problem. This is basically what is described as restructuring. The following example illustrates this:
 * objects, predicates
 * state space
 * operators
 * selection criteria

 * Two boys of different age are playing badminton. The older one is a more skilled player, and therefore it is predictable for the outcome of usual matches who will be the winner. After some time and several defeats the younger boy finally loses interest in playing, and the older boy faces a problem, namely that he has no one to play with anymore.
 * The usual options, according to M. Wertheimer (1945/82), at this point of the story range from 'offering candy' and 'playing another game' to 'not playing to full ability' and 'shaming the younger boy into playing'. All those strategies aim at making the younger stay.
 * And this is what the older boy comes up with: He proposes that they should try to keep the bird in play as long as possible. Thus they change from a game of competition to one of cooperation. They'd start with easy shots and make them harder as their success increases, counting the number of consecutive hits. The proposal is happily accepted and the game is on again.

The key in this story is that the older boy restructured the problem and found out that he used an attitude towards the younger which made it difficult to keep him playing. With the new type of game the problem is solved: the older is not bored, the younger not frustrated.

Possibly, new representations can make a problem more difficult or much easier to solve. To the latter case insight– the sudden realisation of a problem’s solution – seems to be related.

Insight
There are two very different ways of approaching a goal-oriented situation. In one case an organism readily reproduces the response to the given problem from past experience. This is called reproductive thinking.

The second way requires something new and different to achieve the goal, prior learning is of little help here. Such productive thinking is (sometimes) argued to involve insight. Gestalt psychologists even state that insight problems are a separate category of problems in their own right.

Tasks that might involve insight usually have certain features – they require something new and non-obvious to be done and in most cases they are difficult enough to predict that the initial solution attempt will be unsuccessful. When you solve a problem of this kind you often have a so called "AHA-experience" – the solution pops up all of a sudden. At one time you do not have any ideas of the answer to the problem, you do not even feel to make any progress trying out different ideas, but in the next second the problem is solved.

For all those readers who would like to experience such an effect, here is an example for an Insight Problem: Knut is given four pieces of a chain; each made up of three links. The task is to link it all up to a closed loop and he has only 15 cents. To open a link costs 2, to close a link costs 3 cents. What should Knut do?

To show that solving insight problems involves restructuring, psychologists created a number of problems that were more difficult to solve for participants provided with previous experiences, since it was harder for them to change the representation of the given situation (see Fixation). Sometimes given hints may lead to the insight required to solve the problem. And this is also true for involuntarily given ones. For instance it might help you to solve a memory game if someone accidentally drops a card on the floor and you look at the other side. Although such help is not obviously a hint, the effect does not differ from that of intended help.

For non-insight problems the opposite is the case. Solving arithmetical problems, for instance, requires schemas, through which one can get to the solution step by step.

Fixation
Sometimes, previous experience or familiarity can even make problem solving more difficult. This is the case whenever habitual directions get in the way of finding new directions – an effect called fixation.

Functional fixedness
Functional fixedness concerns the solution of object-use problems. The basic idea is that when the usual way of using an object is emphasised, it will be far more difficult for a person to use that object in a novel manner. An example for this effect is the candle problem: Imagine you are given a box of matches, some candles and tacks. On the wall of the room there is a cork-board. Your task is to fix the candle to the cork-board in such a way that no wax will drop on the floor when the candle is lit. – Got an idea?

 * Explanation: The clue is just the following: when people are confronted with a problem and given certain objects to solve it, it is difficult for them to figure out that they could use them in a different (not so familiar or obvious) way. In this example the box has to be recognised as a support rather than as a container.

A further example is the two-string problem: Knut is left in a room with a chair and a pair of pliers given the task to bind two strings together that are hanging from the ceiling. The problem he faces is that he can never reach both strings at a time because they are just too far away from each other. What can Knut do?

 * Solution: Knut has to recognise he can use the pliers in a novel function – as weight for a pendulum. He can bind them to one of the :strings, push it away, hold the other string and just wait for the first one moving towards him. If necessary, Knut can even climb on the chair, but he is not that small, we suppose . ..

Mental fixedness
Functional fixedness as involved in the examples above illustrates a mental set – a person’s tendency to respond to a given task in a manner based on past experience. Because Knut maps an object to a particular function he has difficulties to vary the way of use (pliers as pendulum's weight).

One approach to studying fixation was to study wrong-answer verbal insight problems. It was shown that people tend to give rather an incorrect answer when failing to solve a problem than to give no answer at all.
 * A typical example: People are told that on a lake the area covered by water lilies doubles every 24 hours and that it takes 60 days to cover the whole lake. Then they are asked how many days it takes to cover half the lake. The typical response is '30 days' (whereas 59 days is correct).

These wrong solutions are due to an inaccurate interpretation, hence representation, of the problem. This can happen because of sloppiness (a quick shallow reading of the problem and/or weak monitoring of their efforts made to come to a solution). In this case error feedback should help people to reconsider the problem features, note the inadequacy of their first answer, and find the correct solution. If, however, people are truly fixated on their incorrect representation, being told the answer is wrong does not help. In a study made by P.I. Dallop and R.L. Dominowski in 1992 these two possibilities were contrasted. In approximately one third of the cases error feedback led to right answers, so only approximately one third of the wrong answers were due to inadequate monitoring.

Another approach is the study of examples with and without a preceding analogous task. In cases such like the water-jug task analogous thinking indeed leads to a correct solution, but to take a different way might make the case much simpler:
 * Imagine Knut again, this time he is given three jugs with different capacities and is asked to measure the required amount of water. :Of course he is not allowed to use anything despite the jugs and as much water as he likes. In the first case the sizes are: 127 litres, 21 litres and 3 litres while 100 litres are desired.

 * In the second case Knut is asked to measure 18 litres from jugs of 39, 15 and three litres size.

In fact participants faced with the 100 litre task first choose a complicate way in order to solve the second one. Others on the contrary who did not know about that complex task solved the 18 litre case by just adding three litres to 15.

Problem Solving as a Search Problem
The idea of regarding problem solving as a search problem originated from Alan Newell and Herbert Simon while trying to design computer programs which could solve certain problems. This led them to develop a program called General Problem Solver which was able to solve any well-defined problem by creating heuristics on the basis of the user's input. This input consisted of objects and operations that could be done on them.

As we already know, every problem is composed of an initial state, intermediate states and a goal state (also: desired or final state), while the initial and goal states characterise the situations before and after solving the problem. The intermediate states describe any possible situation between initial and goal state. The set of operators builds up the transitions between the states. A solution is defined as the sequence of operators which leads from the initial state across intermediate states to the goal state.

The simplest method to solve a problem, defined in these terms, is to search for a solution by just trying one possibility after another (also called trial and error).

As already mentioned above, an organised search, following a specific strategy, might not be helpful for finding a solution to some ill-defined problem, since it is impossible to formalise such problems in a way that a search algorithm can find a solution.

As an example we could just take Knut and his essay: he has to find out about his own opinion and formulate it and he has to make sure he understands the sources texts. But there are no predefined operators he can use, there is no panacea how to get to an opinion and even not how to write it down.

Means-End Analysis
In Means-End Analysis you try to reduce the difference between initial state and goal state by creating subgoals until a subgoal can be reached directly (probably you know several examples of recursion which works on the basis of this).

An example for a problem that can be solved by Means-End Analysis are the „Towers of Hanoi“:

Towers of Hanoi – A well defined problem

The initial state of this problem is described by the different sized discs being stacked in order of size on the first of three pegs (the “start-peg“). The goal state is described by these discs being stacked on the third pegs (the “end-peg“) in exactly the same order.

There are three operators:
 * You are allowed to move one single disc from one peg to another one
 * You are only able to move a disc if it is on top of one stack
 * A disc cannot be put onto a smaller one.

In order to use Means-End Analysis we have to create subgoals. One possible way of doing this is described in the picture:

1.  Moving the discs lying on the biggest one onto the second peg.

2.  Shifting the biggest disc to the third peg.

3.  Moving the other ones onto the third peg, too

You can apply this strategy again and again in order to reduce the problem to the case where you only have to move a single disc – which is then something you are allowed to do.

Strategies of this kind can easily be formulated for a computer; the respective algorithm for the Towers of Hanoi would look like this:

1.  move n-1 discs from A to B

2.  move disc #n from A to C

3.  move n-1 discs from B to C

where n is the total number of discs, A is the first peg, B the second, C the third one. Now the problem is reduced by one with each recursive loop.

Means-end analysis is important to solve everyday-problems – like getting the right train connection: You have to figure out where you catch the first train and where you want to arrive, first of all. Then you have to look for possible changes just in case you do not get a direct connection. Third, you have to figure out what are the best times of departure and arrival, on which platforms you leave and arrive and make it all fit together.

Analogies
Analogies describe similar structures and interconnect them to clarify and explain certain relations. In a recent study, for example, a song that got stuck in your head is compared to an itching of the brain that can only be scratched by repeating the song over and over again.

Restructuring by Using Analogies
One special kind of restructuring, the way already mentioned during the discussion of the Gestalt approach, is analogical problem solving. Here, to find a solution to one problem – the so called target problem, an analogous solution to another problem – the source problem, is presented.

An example for this kind of strategy is the radiation problem posed by K. Duncker in 1945:

As a doctor you have to treat a patient with a malignant, inoperable tumour, buried deep inside the body. There exists a special kind of ray, which is perfectly harmless at a low intensity, but at the sufficient high intensity is able to destroy the tumour – as well as the healthy tissue on his way to it. What can be done to avoid the latter?

When this question was asked to participants in an experiment, most of them couldn't come up with the appropriate answer to the problem. Then they were told a story that went something like this:

A General wanted to capture his enemy's fortress. He gathered a large army to launch a full-scale direct attack, but then learned, that all the roads leading directly towards the fortress were blocked by mines. These roadblocks were designed in such a way, that it was possible for small groups of the fortress-owner's men to pass them safely, but every large group of men would initially set them off. Now the General figured out the following plan: He divided his troops into several smaller groups and made each of them march down a different road, timed in such a way, that the entire army would reunite exactly when reaching the fortress and could hit with full strength.

Here, the story about the General is the source problem, and the radiation problem is the target problem. The fortress is analogous to the tumour and the big army corresponds to the highly intensive ray. Consequently a small group of soldiers represents a ray at low intensity. The solution to the problem is to split the ray up, as the general did with his army, and send the now harmless rays towards the tumour from different angles in such a way that they all meet when reaching it. No healthy tissue is damaged but the tumour itself gets destroyed by the ray at its full intensity.

M. Gick and K. Holyoak presented Duncker's radiation problem to a group of participants in 1980 and 1983. Only 10 percent of them were able to solve the problem right away, 30 percent could solve it when they read the story of the general before. After given an additional hint – to use the story as help – 75 percent of them solved the problem.

With this results, Gick and Holyoak concluded, that analogical problem solving depends on three steps:

1. Noticing that an analogical connection exists between the source and the target problem.

2. Mapping corresponding parts of the two problems onto each other (fortress → tumour, army → ray, etc.)

3. Applying the mapping to generate a parallel solution to the target problem (using little groups of soldiers approaching from different directions → sending several weaker rays from different directions)

Next, Gick and Holyoak started looking for factors that could be helpful for the noticing and the mapping parts, for example:

Discovering the basic linking concept behind the source and the target problem.

-->picture coming soon<--

Schema
The concept that links the target problem with the analogy (the “source problem“) is called problem schema. Gick and Holyoak obtained the activation of a schema on their participants by giving them two stories and asking them to compare and summarise them. This activation of problem schemata is called “schema induction“.

The two presented texts were picked out of six stories which describe analogical problems and their solution. One of these stories was "The General" (remember example in Chapter 4.1).

After solving the task the participants were asked to solve the radiation problem (see chapter 4.2). The experiment showed that in order to solve the target problem reading of two stories with analogical problems is more helpful than reading only one story: After reading two stories 52% of the participants were able to solve the radiation problem (As told in chapter 4.2 only 30% were able to solve it after reading only one story, namely: “The General“).

Gick and Holyoak found out that the quality of the schema a participant developed differs. They classified them into three groups:
 * Good schemata: In good schemata it was recognised that the same concept was used in order to solve the problem (21% of the participants created a good schema and 91% of them were able to solve the radiation problem).
 * Intermediate schemata: The creator of an intermediate schema has figured out that the root of the matter equals (here: many small forces solved the problem). (20% created one, 40% of them had the right solution).
 * Poor schemata: The poor schemata were hardly related to the target problem. In many poor schemata the participant only detected that the hero of the story was rewarded for his efforts (59% created one, 30% of them had the right solution).

The process of using a schema or analogy, i.e. applying it to a novel situation is called transduction. One can use a common strategy to solve problems of a new kind.

To create a good schema and finally get to a solution is a problem-solving skill that requires practise and some background knowledge.

How do Experts Solve Problems?
With the term expert we describe someone who devotes large amounts of his or her time and energy to one specific field of interest in which he, subsequently, reaches a certain level of mastery. It should not be of surprise that experts tend to be better in solving problems in their field than novices (people who are beginners or not as well trained in a field as experts) are. They are faster in coming up with solutions and have a higher success rate of right solutions. But what is the difference between the way experts and non-experts solve problems? Research on the nature of expertise has come up with the following conclusions:

 * Experts know more about their field,
 * their knowledge is organised differently, and
 * they spend more time analysing the problem.

When it comes to problems that are situated outside the experts' field, their performance often does not differ from that of novices.

Knowledge: An experiment by Chase and Simon (1973a, b) dealt with the question how well experts and novices are able to reproduce positions of chess pieces on chessboards when these are presented to them only briefly. The results showed that experts were far better in reproducing actual game positions, but that their performance was comparable with that of novices when the chess pieces were arranged randomly on the board. Chase and Simon concluded that the superior performance on actual game positions was due to the ability to recognise familiar patterns: A chess expert has up to 50,000 patterns stored in his memory. In comparison, a good player might know about 1,000 patterns by heart and a novice only few to none at all. This very detailed knowledge is of crucial help when an expert is confronted with a new problem in his field. Still, it is not pure size of knowledge that makes an expert more successful. Experts also organise their knowledge quite differently from novices.

Organisation: In 1982 M. Chi and her co-workers took a set of 24 physics problems and presented them to a group of physics professors as well as to a group of students with only one semester of physics. The task was to group the problems based on their similarities. As it turned out the students tended to group the problems based on their surface structure (similarities of objects used in the problem, e.g. on sketches illustrating the problem), whereas the professors used their deep structure (the general physical principles that underlay the problems) as criteria. By recognising the actual structure of a problem experts are able to connect the given task to the relevant knowledge they already have (e.g. another problem they solved earlier which required the same strategy).

Analysis: Experts often spend more time analysing a problem before actually trying to solve it. This way of approaching a problem may often result in what appears to be a slow start, but in the long run this strategy is much more effective. A novice, on the other hand, might start working on the problem right away, but often has to realise that he reaches dead ends as he chose a wrong path in the very beginning.

Creative Cognition
We already introduced a lot of ways to solve a problem, mainly strategies that can be used to find the “correct” answer. But there are also problems which do not require a “right answer” to be given – It is time for creative productiveness!

Imagine you are given three objects – your task is to invent a completely new object that is related to nothing you know. Then try to describe its function and how it could additionally be used. Difficult? Well, you are free to think creatively and will not be at risk to give an incorrect answer. For example think of what can be constructed from a half-sphere, wire and a handle. The result is amazing: a lawn lounger, global earrings, a sled, a water weigher, a portable agitator, ...

Divergent Thinking
The term divergent thinking describes a way of thinking that does not lead to one goal, but is open-ended. Problems that are solved this way can have a large number of potential 'solutions' of which none is exactly 'right' or 'wrong', though some might be more suitable than others.

Solving a problem like this involves indirect and productive thinking and is mostly very helpful when somebody faces an ill-definedproblem, i.e. when either initial state or goal state cannot be stated clearly and operators or either insufficient or not given at all.

The process of divergent thinking is often associated with creativity, and it undoubtedly leads to many creative ideas. Nevertheless, researches have shown that there is only modest correlation between performance on divergent thinking tasks and other measures of creativity. Additionally it was found that in processes resulting in original and practical inventions things like searching for solutions, being aware of structures and looking for analogies are heavily involved, too.

Thus, divergent thinking alone is not an appropriate tool for making an invention. You also need to analyse the problem in order to make the suggested, i.e. invention, solution appropriate.

right or wrong
The ability of children to imitate the people and the surrounding environment also influential in recognizing the concepts of right and wrong To introduce the concepts of right and wrong must be seen from the age of the child. When children are a year old, their brains are not fully developed so their understanding is still limited. But keep in mind, too, from an early age the average child is able to imitate parents, see their surroundings and do imitation or called modeling. Therefore, the introduction of the concept of right and wrong also depends on how the parents or other adults live with the child. "If a mother often sits on the couch while raising both legs, children tend to sit with more or less the same style and think this is true. As we get older, modeling is the most natural thing that children can get about right and wrong," said this psychologist called Kiki. The method of giving understanding about the concepts of right and wrong is also adjusted to the age of the child. If children are still toddlers, they can go through activities such as telling stories that are rich in social values. Slip conclusions at the end of a fairy tale. "For example, the Kancil tale, after storytelling parents can say, 'So, stealing is not good', to emphasize the moral message in the fairy tale," said the psychologist from the Indonesian Psychological Practice Foundation, Bintaro, South Jakarta. For children who are older, for example in primary school age and still under 12 years of age, understanding can be given by giving an explanation of their eyes. Because the nature of them still tends to be egocentric. However, when entering adolescence, giving an explanation can be through a general perspective, especially cause and effect. "When giving to tell children about the concepts of right and wrong, parents need to pay attention to whether the child really understands the message that was delivered as a whole or only part of the contents of the message," Kiki added. For example, when parents want to teach the concept of stealing is not good through the story of Kancil, parents must make sure the child understands that anyone should not steal, no matter what the circumstances. Do not let the child who understands that is not allowed to steal a mouse deer or that should not be stolen is cucumber. Therefore, ask the child to explain his understanding once more so that the child is sure to understand. Responsible Learning If you have been taught the concept of right and wrong, but the child still violates it, parents must act and the child needs to know the consequences of the wrong actions. "For example, it was explained that you should not pick rambutan from a neighboring tree, but the child still did it, immediately reprimanded firmly and words that were not ambiguous or ambiguous, but still polite. "However, the child must be responsible for his attitude," Kiki reminded. Of course, continued Kiki, all this depends on the age of the child. In a small age for certain things, it is better for parents to stay with children, but when they are older, children need to know that parents will not risk their mistakes. Children who from childhood have understood between right and wrong will grow into individuals who are independent, responsible and well-mannered. This will also make it easier for them to socialize in their environment, have healthy friendships and make it easier for them to get good jobs because employers and coworkers certainly want to work with people who are polite, honest and responsible. Important to remember The following basic things can be done by parents to instill in children the right behavior - To say thanks - Say a word please if you want to ask for help - apologize if wrong, even to the child if the parents are wrong - Say greetings

Convergent Thinking
Convergent thinking patterns are problem solving techniques that unite different ideas or fields to find a solution. The focus of this mindset is speed, logic and accuracy, also identification of facts, reapplying existing techniques, gathering information. The most important factor of this mindset is: there is only one correct answer. You only think of two answers, namely right or wrong. This type of thinking is associated with certain science or standard procedures. People with this type of thinking have logical thinking, are able to memorize patterns, solve problems and work on scientific tests. Most school subjects sharpen this type of thinking ability.

Research shows that the creative process involves both types of thought processes. But experts recommend not joining the two processes in one session. For example, in the next 30 minutes, you invite everyone on your team to brainstorm creating new ideas (which involve divergent thinking patterns). Within 30 minutes, all ideas should only be recorded, not judged, for example by saying that an idea is irrelevant because of a limited budget. After all the ideas are contained, go to the next session, namely analysis and decision making (which involves convergent thinking patterns). Based on research too, doing creative jobs causes mood swings (mood swings), and it turns out that both types of thinking create two different moods. Convergent thinking patterns create negative moods, while divergent thinking patterns create a positive mood. J.A. Research Horne in 1988 revealed that lack of sleep will greatly affect the performance of people with divergent thought patterns, whereas people with convergent mindsets will be more likely to be fine. Including which mindset do you have? Use wisely your talents, and practice both types of thinking to be able to use them in balance at the right times.

Neurophysiological Background
Presenting Neurophysiology in its entirety would be enough to fill several books. Fortunately we do not have to concern ourselves with most of these facts. Instead, let's just focus on the aspects that are really relevant to problem solving. Nevertheless this topic is quite complex and problem solving cannot be attributed to one single brain area. Rather there are systems of several brain areas working together to perform a specific task. This is best shown by an example:

 * In 1994 Paolo Nichelli and coworkers used the method of PET (Positron Emission Tomography), to localise certain brain areas, which are involved in solving various chess problems. In the following table you can see which brain area was active during a specific task:

One of the key tasks, namely planning and executing strategies, is performed by a brain area which also plays an important role for several other tasks correlated with problem solving – the prefrontal cortex (PFC). This can be made clear if you take a look at several examples of damages to the PFC and their effects on the ability to solve problems.

Patients with a lesion in this brain area have difficulty switching from one behaviouristic pattern to another. A well known example is the wisconsin card-sorting task. A patient with a PFC lesion who is told to separate all blue cards from a deck, would continue sorting out the blue ones, even if the experimenter told him to sort out all brown cards. Transferred to a more complex problem, this person would most likely fail, because he is not flexible enough to change his strategy after running into a dead end.

Another example is the one of a young homemaker, who had a tumour in the frontal lobe. Even though she was able to cook individual dishes, preparing a whole family meal was an infeasible task for her.

As the examples above illustrate, the structure of our brain seems to be of great importance regarding problem solving, i.e. cognitive life. But how was our cognitive apparatus designed? How did perception-action integration as a central species specific property come about?

The Evolutionary Perspective
Charles Darwin developed the evolutionary theory which was primarily meant to explain why there are so many different kinds of species. This theory is also important for psychology because it explains how species were designed by evolutionary forces and what their goals are. By knowing the goals of species it is possible to explain and predict their behaviour.

The process of evolution involves several components, for instance natural selection – which is a feedback process that 'chooses' among 'alternative designs' on the basis of deciding how good the respective modulation is. As a result of this natural selection we find adaption. This is a process that constantly tests the variations among individuals in relation to the environment. If adaptions are useful they get passed on; if not they’ll just be an unimportant variation.

Another component of the evolutionary process is sexual selection, i.e. increasing of certain sex characteristics, which give individuals the ability to rival with other individuals of the same sex or an increased ability to attract individuals of the opposite sex.

Altruism is a further component of the evolutionary process, which will be explained in more detail in the following chapter Evolutionary Perspective on Social Cognitions.

Summary and Conclusion
After Knut read this WikiChapter he was relieved that he did not waste his time for the essay – quite the opposite! He now has a new view on problem solving – and recognises his problem as a well-defined one:

His initial state was the clear blank paper without any philosophical sentences on it. The goal state was just in front of his mind's eye: Him – grinning broadly – handing in the essay with some carefully developed arguments.

He decides to use the technique of Means-End Analysis and creates several subgoals:

 * 1. Read important passages again
 * 2. Summarise parts of the text
 * 3. Develop an argumentative structure
 * 4. Write the essay
 * 5. Look for typos

Right after he hands in his essay Knut will go on reading this WikiBook. He now looks forward to turning the page over and to discovering the next chapter...

Organizational Stuff

 * [mailto:anwinkle@uos.de,benkuest@uos.de,lkaestne@uos.de,nmoeller@uos.de,tgrage@uos.de send eMail to all]
 * anwinkle
 * benkuest
 * lkaestne
 * nmoeller
 * tgrage


text:
A-level Physics/Wave properties/Waves

Electromagnetic Waves
The electromagnetic spectrum is a family of waves that share the following properties:

 * They are able to transmit through a vacuum.
 * They all travel at the same speed in a vacuum (3×108 ms−1).
 * They are all transverse waves consisting of magnetic and electric fields oscillating at right angles to each other.
 * They all transfer energy as photons (the higher the frequency of a particular radiation the greater the energy contained in each photon.
 * They can all be reflected, refracted, diffracted and create interference patterns.
 * Properties of these waves change with their frequency / wavelength so they are divided into seven sub groups which are radio wave, microwaves, infra red waves, visible light, ultraviolet, x rays and gamma rays.

Radio Waves

Radio waves are used mainly in communication over short or long distances. Shorter wavelengths are used for television and FM radio while longer wavelengths are used for AM radio.

Long Wave Wavelength = 1*104m  Medium Wave Wavelength = 1*102m  Short Wave Wavelength = 1*100m

Microwaves

Some microwaves pass easily through Earths atmosphere and are used for communications with satellites and or mobile phones.

Microwaves are also commonly used for cooking with the aid of a microwave oven.

Typical Values are as follows: Wavelength (m) = 3*10−2 Frequency (Hz) = 1*1010

Definitions

Transverse Wave  The direction of energy transfer is at 90 degrees to the direction of the vibrating particles.

Longitudinal Wave  The particles vibrate backwards and forwards along the line of the direction of the energy transfer in the wave.

Amplitude  The greatest displacement of the wave.

Period (T)  Is the time taken (in seconds) for one complete cycle of the wave.

Frequency (f)  The number of cycles of the wave per second.

Wavelength (λ)   The shortest distance between 2 particles on the wave with the same phase.

Speed of wave  Distance travelled by the wave in one time period. (λ/T)

title: A-level Physics/Wave properties/Waves


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Cookbook:Curry and Honey Chicken

| Meat Recipes

Due to the experimental birth of this recipe, the measures given are very vague and approximate and can be altered freely. The almonds can be omitted, and if you make your rice a little more interesting (for example: flavouring it with Mexican-ish tomato soup), then you can leave out the vegetable mix altogether.

Marinade

 * 3 tablespoons honey or maple syrup
 * 1 teaspoon curry powder
 * ½–1 cup (120–240 ml) vegetable oil or olive oil
 * Salt (1 heaping teaspoon per kilogram of chicken works well)
 * Chopped parsley or celery leaves (optional)

Main ingredients

 * 4 chicken breasts
 * 1 handful almonds
 * 1 onion or leek
 * 1 red pepper
 * 2–4 tomatoes
 * 1–3 celery greens (if you add more, they can dominate the mix)
 * 1 zucchini or eggplant
 * Other vegetables as desired
 * ½ teaspoon salt or more
 * Cherry tomatoes (optional)
 * Cooked rice

Preparation

 * 1) Combine the ingredients for the marinade. Add chicken and marinate for 6–24 hours; longer is better.
 * 2) Peel almonds by boiling in a small amount of water for 1–2 minutes, cooling, and squeezing the nuts from the skins.
 * 3) Chop onion/leek finely and fry lightly in a large frying pan with a bit of oil.
 * 4) Add vegetables, roughly in the order you find logical (i.e., tomatoes don't take long, zucchini can be in the pan from the start of cooking).
 * 5) Add salt. This will extract water from the vegetables and make them stew faster. You can cover the pan if it goes slowly—this slows the evaporation and allows the vegetables to cook in the water they lose.
 * 6) Dump the cooked vegetables into a bowl or a small pot to keep them warm, and use the remaining oil to fry the cherry tomatoes, if you have those; once done, keep them separate from the other vegetables.
 * 7) Fry almonds gently in the pan.
 * 8) Add chicken meat, and fry on high temperature quickly; when it looks done, cut the largest piece open to see if it is done inside as well. The pieces should be lightly browned. Don't worry, this is the sugar in the honey turning to caramel.
 * 9) Serve meat and vegetables with rice.

Notes, tips, and variations

 * For special occasions, cherry tomatoes will make the meal very interesting (due to the contrast between the sweet chicken, bitter celery and sour tomatoes).
 * Adding cubes of salted and fried mango to the meat just before it's done tastes great. Kiwifruit works too, but not as well. Any sour-ish hard fruit should do the trick. Banana is good too, but it doesn't offer the same contrast.

title: Cookbook:Curry and Honey Chicken


text:
Talk:A-level Physics/Wave properties/Superposition

Specification
From the OCR GCE Physics A specification. Tick with ✔ when you feel each part of the specification has been covered. Try not to add much more than what is in this list as it would not appear in the exam anyway. Use links to wikipedia for more depth in a topic.

 * 1) Explain and use the principle of superposition
 * 2) Understand the term interference
 * 3) Explain the meanings of the terms coherence and path difference
 * 4) Describe experiminets which demonstrate standing (stationary) waves for stretched strings, air columns and microwaves
 * 5) Explain the formation of a standing wave using a graphical method, and identify nodes and antinodes.
 * 6) Explain the meaning of the term diffraction
 * 7) Describe experiments which demonstrate diffraction including the diffraction of water waves in a ripple tank with botha  wide gap and a narrow gap
 * 8) Describe experiments which demonstrate two-source interference in a ripple tank, for light and microwaves
 * 9) Recall and use the equation $$\lambda\ = ax/D$$ for double slit intereference using light


text:
Talk:Card Games/Hearts

Um, why is Shooting the Moon in the variants section? As far as I was aware, it's a pretty universal rule. --Justdig 14:54, 17 April 2006 (UTC)

Contributors to this book may be interested in making Transwiki:Four Corners Solitaire into a book (or part of one). – Mike.lifeguard  | talk 03:13, 13 November 2007 (UTC)

Proposed move
This book only consists of one page. Thus, I propose moving it to Card Games/Hearts, in line with the other games detailed in that book. That is, unless this topic is expected to be significantly expanded. – Adrignola talk 03:15, 8 January 2011 (UTC)
 * Hi, actually I was intending to split the sections up into sub-pages and expand the strategy section over the next few days. I'm not sure what's the custom regarding grouping card games (?), but it seems more logical to me to have it separate (but I'm not well-acquainted with Wikibooks policies). Tempodivalse 03:21, 8 January 2011 (UTC)

 * No policy on it. Theoretically all the subpages of Card Games could be separate books if they were each expanded enough. – Adrignola talk 04:40, 8 January 2011 (UTC)

 * OK, I've moved everything into subpages and will try to expand the existing material. Tempodivalse 16:57, 8 January 2011 (UTC)

title: Talk:Card Games/Hearts


text:
User:K'

Transwiki account. -K' 20:08, 19 May 2006 (UTC)

title: User:K'


text:
User talk:K'

Welcome
Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. Since no one else did :) -K' 13:56, 23 May 2006 (UTC)

title: User talk:K'