text:
Talk:Life of Alexander

Remember that Wikibooks can be a valuable resource. Consider incorporating materials from the School of History resources page, or, if appropriate, adding material to a new Wikibook. Make sure to avoid adding material here that would be more appropriate at Wikibooks or Wikipedia. I think the idea of adding lectures is great! Wikiversity would really shine with some audio or (better yet) video content like that. Anyway, the Department of European History is glad to help out where we can. The Jade Knight 05:35, 3 July 2007 (UTC)

Thucydides: The Peloponnesian War
Perhaps participants from this course are interested in this too ? We have each week chat sessions - until now 12 chat sessions, Erkan Yilmaz uses the Wikiversity:Chat (try) 12:25, 24 March 2008 (UTC)

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

title: Talk:Life of Alexander


text: School talk:Computer Simulation and Game Design


text:
User:Dotty~enwikiversity

My name is Dotty and I am interested in Wikiversity.

title: User:Dotty~enwikiversity


text:
Talk:Advanced Java

= Elements of Good Design =

I'm not sure how advanced this section on advanced Java is supposed to be, but I feel strongly that it should begin with an introduction to OO fundamentals that, while fundamental, are not basic. To ensure it belongs in a Java course, as opposed to a language-agnostic course on object-oriented programming/design/analysis, it should be heavily Java-centric. Also, I feel strongly that it be introduced at the beginning of any discussion of advanced Java topics, as numerous examples of the principles disclosed herein appear throughout the subsequent topics (Collections API, anyone?).

Here is a very brief summary of what I would like to see discussed in the subsections I've included...

Reuse
The compulsion of all new OO programmers is to reuse code with little regard for the proper mechanism of reuse. To set up this course on more advanced topics, I believe it would be invaluable to point up the differences between the different kinds of reuse and when it is appropriate to employ each.

For example, inheritance is not appropriate for semantic reuse, but rather only for behavioral reuse. Though the Shape class and the Cowboy class both define draw methods, that does not mean the behaviors associated with "drawing a shape" and "draw, ya varmint!" are shared—hence it would be inappropriate for these two classes to both implement the same Drawable interface. Drawable.draw could not possibly express a contract of behavior that is common to both shapes and cowboys.

A more subtle and appropriate example: is Square a specific type of Rectangle ? Mathematically, there is no doubt, and many developers would therefore allow Square to extend Rectangle. In most applications (not all, however; context is important) the mathematical truth does not equate to an OO truth. Because the intrinsic characteristic of Square has only one degree of freedom (I'm talking about dimension here, where the degree of freedom defining that characteristic is side length), Rectangle 's dimension characteristic has two degrees of freedom (length and height). Hence, there is no good way to implement Square that extends Rectangle in such a way that a Square could always polymorphically—behaviorally—be treated as a rectangle. One can easily imagine a method that takes a rectangle, sets the width, sets the height, and expects the area to then be equal to the product of the two. Pass this method a square, however, and rectangle-type behavior will not be observed, causing the method to make faulty assumptions about area being the product of the prescribed height and width. Or, imagine a method that attempts to change a rectangle's dimensions to a prescribed aspect ratio while maintaining its area. Good luck getting a square to behave like that!

A second important issue of reuse that should be taught as part of an advanced course is that of aggregation vs. association. (There are many different types of "contains" relationships, but I feel these two are of particular importance and deserve special attention.) The primary difference being: two objects that share an aggregation-type relationship have similar lifetimes because one exists as a "part of" the other. For example, a building "aggregates" a room—without the building that contains it, a room cannot exist. Association is a weaker type of "contains" relation, occurring when two objects become associated with each other for a time but have independent lifetimes. A surgeon "associates" with a scalpel for the duration of a surgery, but there is no whole/part relation here. Before or after a particular runtime scope (an operation), the surgeon need not have access to a scalpel nor a scalpel be used by a surgeon for existence of either to make sense. In contrast, what does it mean to have a building with no rooms, or a room with no building? Interesting philosophical questions, but they should not be explored in the context of an OO system. :-)

The point here is to express that behaviors of objects are expressed by contracts associated with methods, independent of code. Indeed, and interface is useful precisely because it exclusively expresses this contract and prohibits code. Until this clicks misuse of reuse abounds.

(Reference: Liskov Substitution Principle)

Encapsulation
Everyone learns about "information hiding" as part of the basic OO introduction, but very few people really see the point of all those accessors and mutators (getters and setters) that simply get and set fields in one line and do nothing else. Indeed, many of those fields are often declared protected instead of private, and manipulated directly by subclasses.

public class Wrong { // should be private! protected int x;

public Wrong { this(1); }

// should use own setter! public Wrong(int anX) { x = anX; }

public int getX { return x; } public void setX(int anX) { x = anX; }

// ... }

I want to extend Wrong such that whenever x 's value is set, an event is fired off to notify listeners throughout the system...including when its value is initially set. Were this class designed properly, I should be able to override setX and call it a day. However, since this class does not encapsulate its data properly, I cannot be confident in my implementation.

For starters, I'm forced to override both setX and the constructor Wrong(int). If I don't have access to the source code, I can't know that the default no-arg constructor calls Wrong(int) so I have to override that too; in fact, even if I do have access to the source, if I don't override the default no-arg constructor as well my class becomes fragile. If someone were to change the no-arg constructor to simply set x directly instead of forwarding the call to the other constructor, it would seem this could not possibly break anything, yet that's exactly what would happen. Instances of my class that are created by chaining through Wrong 's default no-arg constructor would now no longer behave properly, and listeners would miss out on the initial value of x the instance of my subclass is created.

It seems that overriding both constructors and setX would solve the problem...but, we have to look at the "..." in the code above. If any other method manipulate x directly without going through the setter, my subclass has to override those as well. So much for code reuse through inheritance—it seems my subclass may have to be intimately familiar with the code-level details of how Wrong works, and then override those methods. Furthermore, as features are added to this application we must hope that future changes to other methods leave x alone (or use the setter), lest we have to go back and override those in our subclass.

And we're still not out of the woods! If any developer extends our class, they have direct access to x as well because it was declared protected instead of private! On this count, we're sunk...there's nothing we can do to help our subclasses do the right thing.

It's hard to believe such a simple class can be fraught with so many problems. Much better if it was done right in the first place:

public class Right { private int x;

public Right { this(1); } public Right(int anX) { setX(anX); }

public int getX { return x; } public void setX(int anX) { x = anX; } }

Now, extending Right is a snap: public class SubRight { public void setX(int anX) { super(anX); // notify listeners } }

(Reference: Open-Closed Principle)

Dependency
Most beginners and intermediate developers take a short view of what it means to depend upon another class. If Foo needs to call a method on Bar, it's a simple matter—just obtain access to a Bar instance somehow and call the necessary method.

In reality, it's not quite as simple as that. It is necessary to understand that, first, Bar is an agglomeration of behaviors defined in Bar as well as every class an interface in Bar 's inheritance hierarchy. It is not enough to simply understand the API of the method being called, the developer must ensure that it is being invoked properly within the context of Bar 's entire API. That means understanding every method, the contract defined by Bar as a whole. And since Bar 's contract accumulated from all of the classes and interfaces in its hierarchy, strictly speaking it is necessary to understand those contracts as well.

Bar may seem very simple at first glance, but if it extends a class like javax.servlet.HttpServlet, for example, it also inherits that class' contract that it must be run in a particular kind of container and support participation in a defined lifecycle and anything else true for HttpServlet.

A more immediate example that bites many new Java programmers occurs when they first override equals, defined on java.lang.Object. If one does this without bothering to understand the contract defined on Object, their class will now break in ways both subtle and spectacular, for that contract stipulates that equals must only be overridden in concert with hashCode.

And it doesn't end here...not only does Foo depend on Bar and the classes and interfaces defined in Bar 's hierarchy, but also indirectly on the APIs that Bar uses. This does not seem like a very big deal until one decides that Foo should do all of its logging with the latest version of Apache Commons Logging, only to realize that some class employed by Bar deeply into the dependency graph is using some ancient version of the same package with an incompatible API.

(Reference: Dependency Inversion Principle)

Evolution
So what separates an "advanced" OO developer from a novice? If we review all of the issues addressed above, they all share one thing in common. That is: a novice sees an OO system as something that, one day, will reach a completed state. An advanced developer views an OO system like the corporation or entity that owns it, as a continuing and on-going interest that will never be complete. (It's true; the definition of "corporation" includes the idea of an on-going, indefinite interest.) Indeed, the only OO systems that are ever truly finished are those that have become so unwieldy and unmaintainable because of classes like Wrong that they are scrapped wholesale and reimplemented from the ground up—not by choice, but by necessity.

Advanced developers view code, therefore, as being in a perpetual state of evolution. The more concrete the idea of future direction and requirements for the system, the more intelligence can be built into implementation choices today. Wrong breaks almost immediately upon any attempt at extension. At least Right stands a chance of being around in a few years after requirements have come down the pipeline asking that it (or subclasses of it) manage not just x, but y , z , a HashMap of k s, etc.

(Reference: Stability, Interface Segregation Principle?)

Final Thoughts
I realize this turned out to be not quite as brief as I'd initially intended. What can I say, I get carried away sometimes. Anyway, I will be greatly appreciative if anyone adapts this content for inclusion in the pages themselves. (Or I'll do it myself when I have more time...)

Severoon 07:04, 3 July 2007 (UTC)

= Does Advanced Syntax Section Belong Here? =

I can understand if we kick off Advanced Java with a review of the material covered in the basic and intermediate resources, but should the Advanced Syntax section be covered as a new topic in the advanced topic? It seems to me that all of the basic language features should be covered in beginning (operators, including the bitwise operators covered here) as well as literals and basic math. For instance, the NaN that every beginning coder deals with at some point should be addressed up front, along with integer math—meaning division truncation. Literal representation should be covered there as well, with attention paid to declaring float and long literals, bits, binary/octal/hex notation, etc. These are all very basic, memorization-type activities appropriate for an introductory course on the language.

The intermediate section should cover more advanced language features and Java's support of OO concepts. Language features might include generics (perhaps leaving wildcards for advanced?—maybe not, though, as they're used extensively in the Collections API so it might make sense to cover them earlier rather than later). Support of OO concepts for an intermediate level course might include how Java currently addresses closures (anonymous inner class w/final references), etc.

(Perhaps this isn't the right place to discuss this—if not, please move to the appropriate place and link here. Thanks!)

Severoon 21:27, 6 July 2007 (UTC)

I think that all of the syntactic elements including those that support OO concepts should be taught as early on as possible. I'm not sure what material should be covered in intermediate or advanced Java but it definitely shouldn't be any part of the syntax. Dmclean 12:40, 9 July 2007 (UTC)

Events and GUIs
Wouldn't it make much more sense to learn event-handling as you learn JButtons and other components in the Java Tutorial? I mean, what's the point of a JButton that can't do anything?

title: Talk:Advanced Java


text:
New Zealand Law

The New Zealand Law and Practice Examination (NZLPE) is a self-study examination for overseas practitioners who wish to be admitted to practice in New Zealand. This page will provide learning resources for the NZLPE.

Topics to be covered:
 * /Contract/
 * /Criminal/
 * /Equity/
 * /System/
 * /Property/
 * /Tort/

Official exam materials

 * see NZ Law Society - Exam Materials

title: New Zealand Law


text:
New Zealand Law/Property

Searching Titles

 * Bradley v AG [1978]

Caveats

 * Sims v Lowe
 * Harrison v NZI Bank ltd
 * Holt v Anchorage Mgt
 * Landco Albany v Fu Hao Construction

Indefeasibility of Registered Title

 * Frazer v Walker
 * Davies v Laughton
 * Duncan v McDonald
 * Faulkner v Tauranga DC
 * Bunt v Hallinan
 * Sutton v O’Kane
 * Congregational Christian Church v Broadlands
 * Efstratiou v Glantschnig

Powers of Corrections - ss 80 and 81 LTA
80	Errors in register may be corrected

 * (1) The Registrar may, upon such evidence as appears to him sufficient, subject to any regulations under this Act, correct errors and supply omissions in certificates of title or in the register, or in any entry therein, and may call in any outstanding instrument of title for that purpose.

 * (2) The Registrar may cancel or correct any computer register and, if appropriate, create a new computer register in order to correct any error or supply any omission in any computer register.

81	Surrender of instrument obtained through fraud, etc

 * (1) Where it appears to the satisfaction of the Registrar that any certificate of title or other instrument has been issued in error, or contains any misdescription of land or of boundaries, or that any entry or endorsement has been made in error, or that any grant, certificate, instrument, entry, or endorsement has been fraudulently or wrongfully obtained, or is fraudulently or wrongfully retained, he may require the person to whom that grant, certificate, or instrument has been so issued, or by whom it is retained, to deliver up the same for the purpose of being cancelled or corrected, as the case may require.

 * (2) If the Registrar is satisfied as to any matter referred to in this section and there is a computer register involved, the Registrar may cancel or correct any computer register and, if appropriate, create a new computer register.

 * (3) The Registrar must not take action under subsection (2) without first giving notice to any person appearing to be affected and giving a reasonable period for any response.

Mortgages and Leases

 * Downsview Nominees v First City Corp
 * Neva Hldgs v Wilson
 * Italia Holdings v Lonsdale
 * Fatac Ltd v Commissioner for Inland Revenue
 * Cash Handling v Augustus Terrace
 * Nordern v Blueport

Easements

 * Jansen v Mansor

Encroachment

 * Kingfish Lodge v Archer

Co-ownership

 * Re Foley
 * Fleming v Hargreaves
 * McMahon v McMahon

Joint Family Homes Act 1964

 * The Future of the Joint Family Homes Act, New Zealand Law Commission Report 77 (2001)

Flats, Home Units and Offices

 * Disher v Farnworth

Residential Tenancies Act 1986

 * Residential Tenancies Act 1986 (2003 Reprint)

Maori Land

 * Te Runanganui o Te Kia Whenua v AG
 * AG v Ngati Apa

title: New Zealand Law/Property


text:
New Zealand Law/Tort

Injury Prevention Rehabilitation and Compensation Act 2001

 * Injury Prevention Rehabilitation and Compensation Act 2001

Walbutton v ACC

 * Held
 * An accident is an event that is not intended by the person who suffers the misfortune.

ACC v Mitchell

 * Held
 * There is no need to show that an accident is caused by some external force. (Reversed by s3(a) 1992 Act)

ACC v F

 * Facts
 * Husband sued for depression brought on by wife's injury.

 * Held
 * While the husband's depression was an unlooked for mishap, the husband’s injury was not the relevant accident and mental injury must accompany physical injury.

ACC v E
Facts: E was required by her workplace to undergo a management course by her employer and subsequently suffered suffered mental breakdown.

Held: E was initially turned down for cover under the ACC scheme because it was thought that the scheme only covered mental injury which was accompanied by a physical injury. Court of Appeal overturned the decision, deciding "physical and mental" was to be interpreted generously, to be applied as "physical or mental." This indicates the courts desire to interpret ACC legislation with wide breadth.

Brownlie v Good Health Wanganui (2005) CA

 * Held
 * Non-treatment is as much medical misadventure as negligent treatment

meow

A v Bottril [2003] 2 NZLR 721 (PC)

 * see A v Bottril

Articles

 * Margaret McGregor Vennell "Accident Compensation" [1992] NZ Recent LR 1
 * Manning [1992] NZ Recent LR 10
 * Geoff McLay "Nervous Shock, Tort and Accident Compensation: Tort regained?" (1999) 30 VUWLR 197
 * Manning "Daniels v Thompson: Double Punishment or Double Trouble?" [1998] New Zealand L Rev 721
 * Richard Gaskins "Recalling the Future of ACC" [2000] VUWLR 17
 * Stephen Todd "Exemplary Damages" (1998) 18 NZULR 145
 * Ailsa Duffy "Common Law Response to the Accident Compensation Scheme" [2003] VUWLR 21

Duty of Care

 * Anns v Merton LBC
 * South Pacific v NZ Security
 * Spring v Guardian Assocs
 * Midland Metals v ChCh Press
 * Rolls Royce v CHH

Auditors - Negligent Misstatement

 * Scott Group v McFarlane
 * Caparo v Dickman
 * Boyd Knight v Purdue

Auditors - Other

 * Price Waterhouse v Kwan
 * Deloitte Haskins & Sells v National Mutual Life
 * Wellington District Law Soc v PW

Council liability

 * Anns v Merton LBC
 * Bowen v Paramount Builders
 * Brown v Heathcote CC
 * Murphy v Brentwood DC
 * Invercargill CC v Hamlin
 * Three Meade St v Rotorua DC

Cases v Govt #1

 * X v Bedforshire CC (1995)

 * AG v Prince (1998)

 * Barrett v Enfield LBC (1999)

 * W v Essex CC (2000)
 * B v Attorney-General (2004) 3 NZLR 145 (PC)

Cases v Govt #2

 * A-G v Carter (2003)
 * A-G v Body Corporate (2005)
 * Tai Hobson v A-G (2006)

Nervous Shock

 * Alcock v Chief Constable of South Yorkshire
 * Van Soest v Residentical Health Mgt Unit
 * W v Essex CC

Tort v Contractual Remedies

 * Henderson v Merrett Syndicates
 * Turton v Kuslake
 * Rolls Royce NZ v CH

Limitation Period

 * Invercargill CC v Hamlin

Hunter v Canary Wharf [1997] AC 655

 * Hunter v Canary Wharf

Rylands v Fletcher [1866] LR 1 Ex 265

 * see Rylands v Fletcher

Rickards v Lothian [1913] AC 263

 * Facts
 * An unknown person intentionally blocked a drain on the defendant's property causing water to overflow and damage the plaintiff's stock.

1. An exception to Rylands & Fletcher liability - a person is not responsible for the acts of third parties.
 * Held:
 * 2. Water supply and conveniences are not non-natural uses.

Hamilton v Papakura District Council [2000] 1 NZLR 265

 * see Hamilton v Papakura District Council

Transco PLC v Stockport MBC [2004] 2 AC 1

 * see Transco PLC v Stockport MBC

Statutes

 * Defamation Act 1992

Cases

 * Charleston v News Group Newspapers Ltd [1995] 2 AC 65
 * Mount Cook Group Ltd v Johnstone Motors [1990] 2 NZLR 488
 * Templeton v Jones [1984] 1 NZLR 448
 * Prebble v TVNZ [1994] 3 NZLR 1
 * Jennings v Buchanan [2005] 2 NZLR 577
 * Lange v Atkinson [1998] 3 NZLR 424 (CA)
 * Reynolds v Times Newspapers [1999] 4 All ER 609 (HL)
 * Lange v Atkinson [2000] 1 NZLR 257 (PC)
 * Lange v Atkinson [2000] 3 NZLR 385 (CA)
 * Vickery v McLean (2000) unreported, Court of Appeal, CA 125/00

Privacy

 * Hosking v Runting [2005] 1 NZLR 1
 * TVNZ v Haines (2005), CA 71/04

Vicarious Liability

 * S v Attorney-General [2003] 3 NZLR 450 (CA)
 * W v Attorney-General (2003) unreported, CA 227/02

title: New Zealand Law/Tort


text:
New Zealand Law/Equity

Express Trusts

 * Re Beckbessinger
 * UEB Industries Pension Plan
 * Hall v Guardian Trust
 * Re Singh
 * Fox v Harvey

Statutes

 * Trustee Act 1956 (1995 reprint)

Cases

 * Mendelsohn v Centrepoint Community Trust
 * Hunter v Hunter
 * Greenwood
 * Re Aitken Trusts
 * Jones v AMP Perpetual
 * Stuart v Farmer
 * Te Huango
 * Re Mulligan
 * Re O’Donaghue
 * BNZ v NZ Guardian Trust
 * Foreman v Kingstone

Purpose Trusts

 * Re Filshie
 * Re Budgie

Maori Land Trusts

 * Maori Land Act 1993, Part 12

Types of Trusts

 * putea
 * ahu whenua
 * whanau
 * whenua topu
 * kai tiaki

Statutes

 * Charitable Trusts Act 1957
 * Charities Act 2005

Cases

 * NZ Society of Accountants v CIR
 * CIR v Medical Council
 * Bryant Trust Board v Hamilton CC
 * Chch Orchestra Trust v Smitham
 * Re Twigger
 * Centrepoint Community Growth Trust v CIR
 * Re Mason
 * Morgan v Wgtn City Corp
 * Re Palmerston North Halls Trust Board
 * Re Collier
 * Alacoque v Roche
 * Re Centerpoint Community Growth Trust
 * Wilson Home Trusts
 * Latimer v CIR

Resulting Trusts

 * Bateman TV v Bateman & Thomas
 * General Comms v Development Finance
 * Lankshear v ANZ
 * Re Beckbessinger
 * UEB Industries Pension Plan
 * Hall v Guardian Trust

Equitable Compensation

 * Aquaculture v Green Mussel
 * Cook v Evatt
 * Downview v First City
 * NZ Land Development v Porter
 * A-G v Equiticorp
 * Chirnside v Fay

Constructive Trusts

 * AG for H-K v Reid
 * Avondale v Haggie
 * DFC NZ v Goddard
 * Elders Pastoral v BNZ
 * Equiticorp v AG
 * Equiticorp v Hawkins
 * Fortex v Macintosh
 * Gilles v Keogh,
 * Lankow v Rose
 * Lankshear v ANZ
 * Powell v Thompson
 * Re Newey (Deceased)

Tracing

 * Claytons Case
 * Re Halletts Estate
 * Re Ararimu
 * Re Registered Securities

Equitable Estoppel

 * Burberry Mortgage v Hindsbank
 * Gold Star Insurance v Gamut
 * Prudential v Hawkins

Fiduciaries

 * Day v Mead
 * Elders Pastoral v BNZ
 * Coleman v Myers
 * Clark Boyce v Mouat
 * AG for H-K v Reid
 * Avondale v Haggie
 * Contractors Bonding v Snee
 * Arklow v McLean

Unconscionability

 * Nichols v Jessup
 * O’Connor v Hart
 * Contractors Bonding v Snee
 * AG for E & W v Reid

Rule against perpetuities

 * Perpetuities Act 1964

Wills & Administration

 * Administration Act 1969
 * Simultaneous Deaths Act 195
 * Succession Law: A Succession (Adjustment) Act NZ Law Commission Report No 39 (1997)

Wills: General

 * Wills Act 1837
 * Re Young
 * Re Whyte
 * In re Karsten
 * Tanner v Public Trusteee
 * Re Archibald
 * Brown v Pourau

Mutual Wills

 * Fisher v Mansfield
 * Re Newey (Deceased)

Family Protection Act

 * Family Protection Act 1955
 * Lewis v Cotton
 * Re McLean
 * Williams v Aucutt
 * Re Stewart
 * Re Williams

Law Reform (Testamentary Promises) Act

 * Law Reform (Testamentary Promises) Act 1949
 * Re Welch
 * Rennie v Hamilton

Property (Relationships) Act

 * Property (Relationships) Act
 * Re Williams

title: New Zealand Law/Equity


text:
Trigonometry/Identities

Let us take a right angled triangle with hypotenuse length 1. If we mark one of the acute angles as $$\theta$$, then using the definition of the sine ratio, we have
 * $$\sin \theta = \cfrac{opposite}{hypotenuse}$$

As the hypotenuse is 1,
 * $$\sin \theta = \cfrac{opposite}{1} = opposite$$

Repeating the same process using the definition of the cosine ratio, we have
 * $$\cos \theta = \cfrac{adjacent}{hypotenuse} = \cfrac{adjacent}{1} = adjacent$$

Pythagorean identities
Since this is a right triangle, we can use the Pythagorean Theorem:
 * $$ x^2 + y^2 = r^2$$
 * $$ \frac{x^2}{r^2} + \frac{y^2}{r^2} = \frac{r^2}{r^2} $$
 * $$\operatorname{cos}^2 \theta + \operatorname{sin}^2 \theta = 1$$

This is the most fundamental identity in trigonometry.
 * $$ \frac{x^2}{y^2} + \frac{y^2}{y^2} = \frac{r^2}{y^2} $$
 * $$\operatorname{cot}^2 x + 1 = \operatorname{csc}^2$$

 * $$\frac{x^2}{x^2} + \frac{y^2}{x^2} = \frac{r^2}{x^2}$$
 * $$\operatorname 1 + \operatorname{tan}^2\theta = \operatorname{sec}^2\theta$$

From this identity, if we divide through by squared cosine, we are left with:
 * $$\cfrac{\operatorname{sin}^2 \theta + \operatorname{cos}^2 \theta}{\operatorname{cos}^2 \theta} = \cfrac{1}{\operatorname{cos}^2 \theta}$$
 * $$\operatorname{tan}^2 \theta + 1 = \operatorname{sec}^2\theta$$
 * $$\operatorname{sec}^2 \theta - \operatorname{tan}^2 \theta = 1$$

If instead we divide the original identity by squared sine, we are left with:
 * $$\cfrac{\operatorname{sin}^2 \theta + \operatorname{cos}^2 \theta}{\operatorname{sin}^2 \theta} = \cfrac{1}{\operatorname{sin}^2 \theta}$$
 * $$\operatorname{cot}^2 \theta + 1 = \operatorname{csc}^2 \theta$$
 * $$\operatorname{csc}^2 \theta - \operatorname{cot}^2 \theta = 1$$

There are basically 3 main trigonometric identities. The proofs come directly from the definitions of these functions and the application of the Pythagorean theorem:
 * $$\operatorname{sin}^2 \theta + \operatorname{cos}^2 \theta = 1$$

 * $$\operatorname{sec}^2 \theta - \operatorname{tan}^2 \theta = 1$$

 * $$\operatorname{csc}^2 \theta - \operatorname{cot}^2 \theta = 1$$

Angle sum-difference identities

 * $$\sin(\alpha \pm \beta)=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta$$
 * $$\cos(\alpha \pm \beta)=\cos \alpha\cos \beta\mp \sin \alpha \sin \beta$$

Cofunction identities

 * $$\cos(90-\theta)=\sin\theta$$
 * $$\sec(90-\theta)=\csc\theta$$
 * $$\tan(90-\theta)=\cot\theta$$

 * $$\sin(90-\theta)=\cos\theta$$
 * $$\csc(90-\theta)=\sec\theta$$
 * $$\cot(90-\theta)=\tan\theta$$

Multiple angle identities

 * $$\cos2A=\cos^2A-\sin^2A$$
 * $$\sin2A=2\sin A\cos A$$
 * $$\sin 2\theta= \frac{tan 2\theta*tan\theta}{tan 2\theta-tan\theta} $$
 * $$\cos 2\theta=\frac{tan \theta}{tan 2\theta - tan\theta}$$
 * $$\tan 2\theta=tan\theta(\frac{1}{cos 2\theta}+1)$$
 * $$\tan 2\theta=\frac{2sin^2\theta}{sin 2\theta-tan\theta}$$

title: Trigonometry/Identities


text:
User talk:Severoon

Hello Severoon, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 13:37, 3 July 2007 (UTC)

title: User talk:Severoon


text:
BCP/Aesculus parviflora

Aesculus parviflora

title: BCP/Aesculus parviflora


text:
Category:Generalism

 * School:Advanced General Studies

title: Category:Generalism


text:
User:LOGOSOPHIA

Hi, my name is George. I have two degrees: one in Accounting from Linfield College and the other in History with a minor in Philosophy from Portland State University. My interests include Science, Mathematics, Philosophy, literature and economics. I am an accountant because I love numbers. My major area of concentration is in the History of Ideas. How do and how did we think of the things we think about and what reason do we have for believing them to be more true than other things?

My current reading is "Annals of the Former World" by John McPhee, a history of the Ancient World by Susan Bauer, The Yiddish Policeman's Union by Michael Cabon, American Gods by Neil Gaiman and Six Not So Easy Pieces by Richard Feynman.

Books I recommend: In Philosophy: Being and Time by Heidegger, Logico-Philosophicus by Wittgenstein, Essays in Existentialism by Sartre, Contigency, Irony, Solidarity by Richard Rorty, Studies in Words by Paul Grice. Anything that makes you look at the world differently. Learning something new everyday.

title: User:LOGOSOPHIA


text:
File:Bryse animation example.png

Summary
I made this for Landscape rendering.

title: File:Bryse animation example.png


text:
File:Bryce example animation.ogg

Summary
I made this for Landscape rendering.

title: File:Bryce example animation.ogg


text:
User talk:LOGOSOPHIA

Hello LOGOSOPHIA, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
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Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 23:10, 3 July 2007 (UTC)

title: User talk:LOGOSOPHIA


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Health

Health might well be described as being 'in the eye of the beholder'. An attempt at a global definition was made by the World Health Organisation (1948) : "Health is a complete state of physical, mental and social wellbeing, not merely the absence of disease or infirmity". The need for the latter part of this definition stems from the recognition that, over the last couple of centuries in 'Western-led' societies, discussion about health has been dominated by medically-based professionals (seeing health in terms of whether a diagnosed condition is present, in a body or mind seen distinctly from the rest of people's lives). Sociologists identify how different social groups 'construct' their own understandings of health, and how medics are one social group (albeit a powerful one) amongst many. Other social groups and cultures can also perceive health as related to, eg. individual coping, social support, ecologism, spirituality etc. --Different kinds of definitions are useful in various contexts e.g. functional health is a good approach to evaluate the health of eldery people or work ability -- The problem raised by this is : 'If we have no simple definition of health, how can we know if we are improving it?". Health promotion specialists respond to this by a) accepting people's multiple perceptions of health, often combined in a 'holistic' way, and b) seeking to enable local people to take greater control over their health, as the experts in their own lives, alongside the generalised expertises of the various health professionals. (initial entry by Aldo Mussi, University of Central England, Birmingham, Britain.)

Perceived health has epidemiologically shown to be a powerful predictor for future such as death.

Practicing health
There are many ways to practice health. It depends on what you want to be healthy about.

Germs
Germs are everywhere. Some are harmless, some are harmful, and some are even helpful. Here are 5 ways to protect yourself from germs. (The bad kind.)
 * 1) Wash Your Hands
 * 2) Bathe Often
 * 3) Cover Your Mouth When You Cough or Sneeze
 * 4) Develop an Awareness of Germs, not a Fear
 * 5) Avoid Very Sick People

Sexual health
Sexual activity presents a risk for transferring Sexually transmitted diseases (or 'STDs'), so care should be taken to prevent interaction with bodily fluids (e.g. semen, pre-ejaculate, and the vagina's natural lubricant), as well as skin-to-skin contact with any infected area.

 * Use barriers, such as condoms and dental dams. They are the most effective way to prevent STDs, by preventing interaction with bodily fluids and reducing skin-to-skin contact.
 * Oral and anal sex still require a barrier, despite them not posing a pregnancy risk, as STDs can develop in the mouth and anus as well as the vagina and penis.
 * Ensure that both partners are fully aroused and prepared before any penetration. Trying to penetrate the vagina or anus without proper preparation and lubrication (natural or otherwise) can cause damage that can include bleeding and infection. Communication with your partner is extremely important for this.
 * Dispose of semen and condoms properly.
 * Wash your hands and sheets after.

Be aware that there is no way to ensure 100% protection from infection or pregnancy during intercourse, but if used properly only 2 out of every 100 women using condoms will become pregnant in an entire year. Their effectiveness for preventing STD transmission ranges from 70%-95% depending on what STD and what study you look at. In order to maintain their effectiveness, don't store them in places with extreme temperatures or sharp objects, and be careful not to let latex barriers come into contact with oil-based lubricants or lotions, such as petroleum jelly.

Measuring health

 * General Health Questionnaire (GHQ-28; Goldberg & Hillier, 1979)

Health information

 * UserMeds - Resource for consumers, physicians, nurses, and educators. Includes news, user discussion.
 * NHS Choices UK site for impartial advice on personal health. Includes resources for sexual health.

Essays
These are user essays on health issues. Content is not necessarily reviewed for neutrality or accuracy. If unsigned, anyone may edit them.

title: Health


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Portal talk:Arabic/Arabic stream

124.81.8.203 05:05, 4 July 2007 (UTC)im a student of bilingual school, im used to talk both in arabic well,i want learn arabic more but i dont mind to teach some

title: Portal talk:Arabic/Arabic stream


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BCP/Tradescantia virginiana

Tradescantia virginiana

title: BCP/Tradescantia virginiana


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User talk:Franz Xaver

Hi Franz! Good to see you :). Rather than dropping it on your page, here's the Welcome... it's one of those big boxy things.

I'm actually uploading a few more unidentified plants this morning, thanks for the ID on the Cardamine... looks to be right on the mark! --SB_Johnny | talk 09:39, 4 July 2007 (UTC)

title: User talk:Franz Xaver


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BCP/Lythrum salicaria

Lythrum salicaria

title: BCP/Lythrum salicaria


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BCP/Ailanthus altissima

Ailanthus altissima

title: BCP/Ailanthus altissima


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BCP/Albizia julibrissin

Albizia julibrissin

title: BCP/Albizia julibrissin


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BCP/Platycodon grandiflorus

Platycodon grandiflorus

title: BCP/Platycodon grandiflorus


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User:Franz Xaver

See also de:w:Benutzer:Franz_Xaver.

title: User:Franz Xaver


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Bloom Clock/Category inclusion

One of the major goals of the Bloom Clock is to define when a plant is blooming in any given region of the world. During the initial phases of making this determination, plants are categorized according to when they can be seen blooming in particular geographic regions. The inclusion rule for these categories is simple: if a plant is recorded blooming in a region, then it should be categorized as such.

For consistency, these regional categories should be in the form, with REGION replaced by a shortcut for the region in question, and by the numerical month. See, for example, Category:Bloom Clock/Southeastern Pennsylvania Categories.

These categories can then be used to create "graphical lists" using DynamicPageList. See, for example, Bloom Clock/Keys/Southeastern Pennsylvania/May/White Flowers (created using Category:White flowered plants and Category:BCP/SEPA/5).

As data is accumulated over time from many regions, there could be hundreds (or even thousands) of categories on each log page.

title: Bloom Clock/Category inclusion


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Bloom Clock/Keys/Southeastern Pennsylvania/July/White Flowers/DPL

This page is used to help create a graphical list.

 category=White flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Yellow Flowers/DPL

This page is used to help create a graphical list.

 category=Yellow flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Purple Flowers/DPL

This page is used to help create a graphical list.

 category=Purple flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Pink Flowers/DPL

This page is used to help create a graphical list.

 category=Pink flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Orange Flowers/DPL

This page is used to help create a graphical list.

 category=Orange flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Blue Flowers/DPL

This page is used to help create a graphical list.

 category=Blue flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Red Flowers/DPL

This page is used to help create a graphical list.

 category=Red flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Green Flowers/DPL

This page is used to help create a graphical list.

 category=Green flowered plants category=BCP/SEPA/7 order=descending ordermethod=lastedit


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Bloom Clock/Keys/Southeastern Pennsylvania/July/White Flowers

The plants pictured below have been recorded as blooming during the month of July in Southeastern Pennsylvania.

last updated 11:20, 19 October 2007 (UTC) with 80 plants


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Bloom Clock/Keys/Southeastern Pennsylvania/July/Yellow Flowers

The plants pictured below have been recorded as blooming during the month of July in Southeastern Pennsylvania.

last updated 11:25, 19 October 2007 (UTC) with 40 plants


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Bloom Clock/Welcome

Welcome to the Bloom Clock, Wikiversity's oldest research project! The Bloom Clock serves 3 related functions:

 * 1) Developing a database of when plants bloom in any given geographical region.
 * 2) Helping to teach users about plants, by allowing them to visually identify flowers they saw blooming on a given day
 * 3) Serving as an organizing point for the improvement of wikimedia content (Wikipedia articles, Wiktionary definitions, Commons galleries, Wikibooks chapters, etc.)

How to participate
There are a number of ways to participate, appropriate for all knowledge levels regarding both plants and the use of wikis.

 * 1) Users with little knowledge about plants (or even users who know a lot about them, but don't know every plant) can browse by color, form, and season using the ../Keys/. If the plant you saw isn't on the appropriate list (and you have a photo), try using the ../Unknown plants/ page.
 * 2) Users with a solid knowledge of plants can help identify images on the ../Unknown plants/ page, and log plants they've seen blooming either on the ../Log pages/ or the text list for the current clock run.
 * 3) Users with wiki-editing skills can help create ../Log pages/ and keep the ../Keys/ up-to-date.

title: Bloom Clock/Welcome