Piphilology

 

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PiphilologyΖαζ(π(π(εστριονεύε

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Part of a series of articles on the
mathematical constant π
3.1415926535897932384626433...
Uses
Area of a circle Circumference Use in other formulae
Properties
Irrationality Transcendence
Value
Less than 22/7 Approximations Memorization
People
Archimedes Liu Hui Zu Chongzhi Aryabhata Madhava Jamshīd al-Kāshī Ludolph van Ceulen François Viète Seki Takakazu Takebe Kenko William Jones John Machin William Shanks Srinivasa Ramanujan John Wrench Chudnovsky brothers Yasumasa Kanada
History
Chronology A History of Pi
In culture
Legislation Pi Day
Related topics
Squaring the circle Basel problem Six nines in π Other topics related to π
v t e

Piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant π. The word is a play on the word "pi" itself and of the linguistic field of philology.

There are many ways to memorize π, including the use of piems (a portmanteau, formed by combining pi and poem), which are poems that represent π in a way such that the length of each word (in letters) represents a digit.^[1] Here is an example of a piem: "Now I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics." Notice how the first word has three letters, the second word has one, the third has four, the fourth has one, the fifth has five, and so on. In longer examples, 10-letter words are used to represent the digit zero, and this rule is extended to handle repeated digits in so-called Pilish writing. The short story "Cadaeic Cadenza" records the first 3,834 digits of π in this manner, and a 10,000-word novel, Not A Wake, has been written accordingly.^[2]

However, poems prove to be inefficient for large memorizations of π. Other methods include remembering patterns in the numbers (for instance, the year 1971 appears in the first fifty digits of π) and the method of loci (which has been used to memorize π to 67,890 digits).^[3]

| و

Que j’aime à faire apprendre un nombre utile aux sages ! Immortel Archimède, artiste ingénieur, Qui de ton jugement peut priser la valeur ? Pour moi, ton problème eut de pareils avantages. Jadis, mystérieux, un problème bloquait Tout l’admirable procédé, l’œuvre grandiose Que Pythagore découvrit aux anciens Grecs. Ô quadrature ! vieux tourment du philosophe ! Insoluble rondeur, trop longtemps vous avez Défié Pythagore et ses imitateurs. Comment intégrer l’espace plan circulaire ? Former un triangle auquel il équivaudra ? Nouvelle invention : Archimède inscrira Dedans un hexagone ; appréciera son aire, Fonction du rayon. Pas trop ne s’y tiendra : Dédoublera chaque élément antérieur ; Toujours de l’orbe calculée approchera ; Définira limite ; enfin, l’arc, le limiteur De cet inquiétant cercle, ennemi trop rebelle ! Professeur, enseignez son problème avec zèle !

COUNTUNIQUEIFS

Returns the unique count of a range depending on multiple criteria.

Sample Usage

COUNTUNIQUEIFS(A2:A10, B2:B10, ">20")

COUNTUNIQUEIFS(A2:A10, B2:B10, ">20", C2:C10, "<30")

COUNTUNIQUEIFS(A2:A10, D2:D10, "Yes")

Parts of a COUNTUNIQUEIFS function

COUNTUNIQUEIFS(count_unique_range, criteria_range1, criterion1, [criteria_range2, criterion2, ...])

Part	Description
count_unique_range	The range from which the unique values will be counted.
criteria_range1	The range to check against criterion1.
criterion1	The pattern or test to apply to criteria_range1.
Criteria_range2, criterion2, …	[OPTIONAL] - Additional ranges and criteria to check.

Notes

• COUNTUNIQUEIFS will return 0 if none of the criterion are satisfied.
• count_unique_range and all the criterion ranges must contain the same number of rows and columns.

Examples

Related functions

• COUNTUNIQUE
• COUNTIFS
• IF
• AVERAGEIFS
• MAXIFS
• SUMIFS

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| دانشمندان

.ره

| سرمنزل

| مقصود

| بما

| آموزد How I like to teach this number useful to the wise.

Immortal Archimedes, artist, engineer,

in your opinion who could estimate its value?

For me, your problem had equal advantages.

Long ago, mysterious, a problem blocked

All the admirable process, the great work

That Pythagoras revealed to the Ancient Greeks.

Oh quadrature! Old philosopher's torment

Unsolvable roundness, for too long you have

Defied Pythagoras and his imitators.

How to integrate the plain circular space?

Form a triangle to which it is equivalent?

New invention: Archimedes will inscribe

Inside a hexagon; will appreciate its area

Function of a ray. Not too much to hold onto there:

Will split each previous element;

Always the calculated orb will approach

Will define the limit; finally, the arc, the limiter

Of this disturbing circle, an enemy too rebellious

Teacher, teach its problem with zeal

Visual angle is the angle a viewed object subtends at the eye, usually stated in degrees of arc. It also is called the object's angular size.

The diagram on the right shows an observer's eye looking at a frontal extent (the vertical arrow) that has a linear size ${\displaystyle S}$, located in the distance ${\displaystyle D}$ from point ${\displaystyle O}$.

For present purposes, point ${\displaystyle O}$ can represent the eye's nodal points at about the center of the lens, and also represent the center of the eye's entrance pupil that is only a few millimeters in front of the lens.

The three lines from object endpoint ${\displaystyle A}$ heading toward the eye indicate the bundle of light rays that pass through the cornea, pupil and lens to form an optical image of endpoint ${\displaystyle A}$ on the retina at point ${\displaystyle a}$. The central line of the bundle represents the chief ray.

The same holds for object point ${\displaystyle B}$ and its retinal image at ${\displaystyle b}$.

The visual angle ${\displaystyle V}$ is the angle between the chief rays of ${\displaystyle A}$ and ${\displaystyle B}$.

Contents

• 1Measuring and computing
• 2The retinal image and visual angle
• 3Examples
• 4Terminological confusions
• 5Representation of visual angle in visual cortex
• 6See also
• 7Notes
• 8References
• 9External links

Measuring and computing