What is "rule of three"

Rule \Rule\, n. [OE. reule, riule, OF. riule, reule, F. r['e]gle, fr. L. regula a ruler, rule, model, fr. regere, rectum, to lead straight, to direct. See Right, a., and cf. Regular.]

1. That which is prescribed or laid down as a guide for conduct or action; a governing direction for a specific purpose; an authoritative enactment; a regulation; a prescription; a precept; as, the rules of various societies; the rules governing a school; a rule of etiquette or propriety; the rules of cricket.

   We profess to have embraced a religion which contains the most exact rules for the government of our lives.
   --Tillotson.

2. Hence:

   1. Uniform or established course of things.

      'T is against the rule of nature.
      --Shak.

   2. Systematic method or practice; as, my ule is to rise at six o'clock.

   3. Ordibary course of procedure; usual way; comon state or condition of things; as, it is a rule to which there are many exeptions.

   4. Conduct in general; behavior. [Obs.]

      This uncivil rule; she shall know of it.
      --Shak.

3. The act of ruling; administration of law; government; empire; authority; control.

   Obey them that have the rule over you.
   --Heb. xiii. 17.

   His stern rule the groaning land obeyed.
   --Pope.

4. (Law) An order regulating the practice of the courts, or an order made between parties to an action or a suit.
   --Wharton.

5. (Math.) A determinate method prescribed for performing any operation and producing a certain result; as, a rule for extracting the cube root.

6. (Gram.) A general principle concerning the formation or use of words, or a concise statement thereof; thus, it is a rule in England, that s or es, added to a noun in the singular number, forms the that noun; but ``man'' forms its plural ``men'', and is an exception to the rule.

7. 1. A straight strip of wood, metal, or the like, which serves as a guide in drawing a straight line; a ruler.

   2. A measuring instrument consisting of a graduated bar of wood, ivory, metal, or the like, which is usually marked so as to show inches and fractions of an inch, and jointed so that it may be folded compactly.

      A judicious artist will use his eye, but he will trust only to his rule.
      --South.

8. (Print.)

   1. A thin plate of metal (usually brass) of the same height as the type, and used for printing lines, as between columns on the same page, or in tabular work.

   2. A composing rule. See under Conposing.

      As a rule, as a general thing; in the main; usually; as, he behaves well, as a rule.

      Board rule, Caliber rule, etc. See under Board, Caliber, etc.

      Rule joint, a knuckle joint having shoulders that abut when the connected pieces come in line with each other, and thus permit folding in one direction only.

      Rule of the road (Law), any of the various regulations imposed upon travelers by land or water for their mutual convenience or safety. In the United States it is a rule of the road that land travelers passing in opposite directions shall turn out each to his own right, and generally that overtaking persons or vehicles shall turn out to the left; in England the rule for vehicles (but not for pedestrians) is the opposite of this.

      Rule of three (Arith.), that rule which directs, when three terms are given, how to find a fourth, which shall have the same ratio to the third term as the second has to the first; proportion. See Proportion, 5 (b) .

      Rule of thumb, any rude process or operation, like that of using the thumb as a rule in measuring; hence, judgment and practical experience as distinguished from scientific knowledge.

Three \Three\, n.

1. The number greater by a unit than two; three units or objects.

2. A symbol representing three units, as 3 or iii.

   Rule of three. (Arith.) See under Rule, n.

alt. 1 (context mathematics education English) A rule stating that, if two ratios are equal, then the denominator of the second equals its numerator times the reciprocal of the first ratio: if $frac\; ab=frac\; cd$ then $d=frac\{bc\}a$. 2 (context medicine English) A rule for clinical trials used for determining the rate of adverse side effects when no such side effects present during the course of the trial. 3 (context writing rhetoric English) A rule which states that things which come in groups of three are inherently funnier or more effective than things which come in groups of other sizes. 4 (context religion Wicca English) A religious tenet stating that the energy a person puts out into the world, positive or negative, will be returned to that person three times. n. 1 (context mathematics education English) A rule stating that, if two ratios are equal, then the denominator of the second equals its numerator times the reciprocal of the first ratio: if $frac\; ab=frac\; cd$ then $d=frac\{bc\}a$. 2 (context medicine English) A rule for clinical trials used for determining the rate of adverse side effects when no such side effects present during the course of the trial. 3 (context writing rhetoric English) A rule which states that things which come in groups of three are inherently funnier or more effective than things which come in groups of other sizes. 4 (context religion Wicca English) A religious tenet stating that the energy a person puts out into the world, positive or negative, will be returned to that person three times.

Rule of three may refer to:

The rule of three and rule of five are rules of thumb in C++ for the building of exception-safe code and for formalizing rules on resource management. It accomplishes this by prescribing how the default members of a class should be used to accomplish this task in a systematic manner.

The Rule of Three (also Three-fold Law or Law of Return) is a religious tenet held by some Wiccans/Pagans. It states that whatever energy a person puts out into the world, be it positive or negative, will be returned to that person three times. Some subscribe to a variant of this law in which return is not necessarily threefold.

The Rule of Three is sometimes described as karma by Wiccans, however this is not strictly accurate. Both concepts describe the process of cause and effect and often encourage the individual to act in a good way. However the concept of karma, according to the scriptures of Buddhism, Hinduism and other eastern belief systems, does not operate on a system of three-fold return. According to some traditions, the rule of three is not literal but symbolizes that our energy returns our way as many times as needed for us to learn the lesson associated with it.

According to John Coughlin the Law posits "a literal reward or punishment tied to one's actions, particularly when it comes to working magic". The law is not a universal article of faith among Wiccans, and "there are many Wiccans, experienced and new alike, who view the Law of Return as an over-elaboration on the Wiccan Rede." Some Wiccans believe that it is a modern innovation based on Christian morality.

The Rule of Three has been compared by Karl Lembke to other ethics of reciprocity, such as the concept of karma in Dharmic religions and the Golden Rule

The Rule of Three has a possible prototype in a piece of Wiccan liturgy which first appeared in print in Gerald Gardner's 1949 novel High Magic's Aid:

However, The Threefold Law as an actual "law", was an interpretation of Wiccan ideas and ritual, made by Monique Wilson and further popularized by Raymond Buckland, in his books on Wicca. Prior to this innovation by Wilson and its subsequent inclusion in publications, Wiccan ideas of reciprocal ethics were far less defined and more often interpreted as a kind of general karma.

The first published reference to the Rule of Three as a general ethical principle may be from Raymond Buckland, in a 1968 article for Beyond magazine. The Rule of Three later features within a poem of 26 couplets titled "Rede of the Wiccae", published by Lady Gwen Thompson in 1975 in Green Egg vol. 8, no. 69 and attributed to her grandmother Adriana Porter. The threefold rule is referenced often by the Wiccans of the Clan Mackenzie in the S.M. Stirling Emberverse novels.

This rule was described by the Dutch metal band Nemesea, in the song "Threefold Law", from the album Mana.

The rule of three or power of three is a writing principle that suggests that things that come in threes are funnier, more satisfying, or more effective than other numbers of things. The reader or audience of this form of text is also thereby more likely to remember the information. This is because having three entities combines both brevity and rhythm with having the smallest amount of information to create a pattern. It makes the author or speaker appear knowledgeable while being both simple and catchy.

Slogans, film titles and a variety of other things have been structured in threes, a tradition that grew out of oral storytelling. Examples include the Three Little Pigs, Three Billy Goats Gruff, and the Three Musketeers. Similarly, adjectives are often grouped in threes to emphasize an idea.

The Latin phrase, "omne trium perfectum" (everything that comes in threes is perfect, or, every set of three is complete) conveys the same idea as the rule of three.

In aviation, the rule of three or "3:1 rule of descent" is that 3 miles of travel should be allowed for every of descent.

In the early days of aviation, few aircraft were pressurized. A pilot who descended rapidly would cause his passengers the discomfort of rapid pressure changes on their eardrums.

Transport pilots adopted this formula to assure a slow, steady and comfortable descent for their passengers. Many aircraft had a cruising speed between . Three miles would be traveled in about 1.5–1.8 minutes, resulting in a rate of descent of about 550–660 feet per minute. That was about as fast as passengers could comfortably adapt to the changing pressure on their eardrums. However, many pilots used a 300-feet-per-minute descent rate because doing so is almost unnoticed by passengers. A pilot cruising at 10,500 feet would calculate that in order to be at 1,000 feet at his destination, he would have to descend 9,500 feet. Dividing 9,500 feet by 300 feet per minute, that descent would require about 32 minutes. If his ground speed was , he would begin his descent about from his destination (traffic permitting).

The "rule of three" is used by pilots flying small, unpressurized aircraft as well as by those flying airliners and aircraft with pressurized cabins. These usually fly in a structured environment governed by instrument flight rules (IFR) and may not have the luxury of choosing a descent rate, instead observing the altitude constraints assigned to them by air traffic controllers. Although rate of cabin pressurization change may be a consideration, this is usually managed automatically and for an airliner a larger consideration is fuel economy. A 3:1 descent gives an efficient glide descent from cruising altitude, and aids in planning; the company standard descent speed will be close to (usually slightly higher than) the optimum Lift/Drag ratio speed, and will give a descent ratio close to 3:1.

An additional use of this rule-of-thumb is on final approach which generally has a 3 degree vertical angle. This corresponds to 3 nautical miles (nm) per 1000ft and again makes mental estimation simple.

Rule of three is a code refactoring rule of thumb to decide when a replicated piece of code should be replaced by a new procedure. It states that the code can be copied once, but that when the same code is used three times, it should be extracted into a new procedure. The rule was introduced by Martin Fowler in Refactoring and attributed to Don Roberts.

Duplication in programming is a bad practice because it makes the code harder to maintain. However, code refactoring to eliminate duplication also takes time, which might be better spent on other tasks. Triplication has an even higher cost because it makes maintenance harder yet. When the rule encoded in a replicated piece of code changes, whoever maintains the code will have to change it in all places correctly. This process is error-prone and often leads to problems. If the code exists in only one place, then it can be easily changed there. The rule proposes that the cost of maintenance certainly outweighs the cost of refactoring when there are three copies, and may or may not if there are two copies.

As Charles Petzold puts it, "Three or more? Use a for!"

In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects ($\hat p=0$), the interval from 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation to results from more sensitive tests. For example, a pain-relief drug is tested on 1500 human subjects, and no adverse event is recorded. From the rule of three, it can be concluded with 95% confidence that fewer than 1 person in 500 (or 3/1500) will experience an adverse event. By symmetry, one could expect for only successes ($\hat p=1$), the 95% confidence interval is .

The rule is useful in the interpretation of clinical trials generally, particularly in phase II and phase III where often there are limitations in duration or statistical power. The rule of three applies well beyond medical research, to any trial done n times. If 300 parachutes are randomly tested and all open successfully, then it is concluded with 95% confidence that fewer than 1 in 100 parachutes with the same characteristics (3/300) will fail.There are other meanings of the term "rule of three" in mathematics, and a further distinct meaning within statistics:

A century and a half ago Charles Darwin said he had "no Faith in anything short of actual measurement and the Rule of Three," by which he appeared to mean the peak of arithmetical accomplishment in a nineteenth-century gentleman, solving for x in "6 is to 3 as 9 is to x." Some decades later, in the early 1900s, Karl Pearson shifted the meaning of the rule of three – "take 3σ [ three standard deviations] as definitely significant" – and claimed it for his new journal of significance testing, Biometrika. Even Darwin late in life seems to have fallen into the confusion. (Ziliak and McCloskey, 2008, p. 26; parenthetic gloss in original)

The rule of three in Business and Economics is a rule of thumb suggesting that there are always three major competitors in any free market within any one industry. This was put forward by Bruce Henderson of the Boston Consulting Group in 1976, and has been tested by Jagdish Sheth and Rajendra Sisodia in 2002, analyzing performance data and comparing it to market share. This is an attempt to explain how, in mature markets, there are usually three 'major players' in a competitive market.

The rule of three as put forward by Sheth and Sisodia in 2002 states that in a mature market, there will normally be three major competitors and several others, who only succeed if they are able to operate in a niche market. They based their studies on a review of a number of markets in North America. They compared market share to financial performance, and found that small, niche-market specialists and large, full-line generalists were those who performed best when holding a large market share. They also noticed a section in between the two in which companies performed poorly, which they referred to as “the ditch” (see reference); this is based on the form of the graph of market share versus financial performance as the graph slopes downwards for niche players (1% - 5% market share) and upwards for full-line generalists (over 10% market share). Sheth and Sisodia use the analogy of a shopping mall, in which they propose that there will be three major full-line generalist stores, along with various smaller, product and market specialist shops.

Sheth and Sisodia also make a number of observations with regard to how companies behave in such cases. For instance, the first-ranked player will often be the least innovative in spite of spending the most on R&D. However, the first-ranked player may 'steal' ideas from the third-ranked player.

It may be the case that, if a price war emerges between the first-ranked and second-ranked players, the third-ranked player may end up in “the ditch”, although a new third-rank player would be expected to emerge in due course.

Using a diverse sample of more than 160 US industries, two base-time periods, and numerous performance measures, Uslay, Altintig, and Winsor (2010) empirically tested the rule of three and reported that industries with exactly three generalists outperformed every other industry structure. They also found that micro-specialists, generalists with excessive market share, and firms "in the ditch" without clear strategic strengths tended to underperform others. Their findings provided empirical support for the “Rule of Three”.