OpenLLM-France/wikimedia huggingface dataset:
# Programmed Math/Pythagorean theorem

The pythagorean (pi-THA-gor-in) theorem is a formula which explains the relationship between sides of a right triangle (a triangle w/ one 90 degree angle)
Formula:
$a^{2}+b^{2}=c^{2}$ where a and b are the legs and c is the hypoteneuse.
There is also a thing called a Pythagorean Triple, where in $a^{2}+b^{2}=c^{2}$ a and b are equal to c.
Such an example is with $3^{2}+4^{2}=c^{2}$ Where $3^{2}=9$ and $4^{2}=16,16+9=5^{2}$ which is 25
# Programmed Math/Commutative

An operation is commutitive if and only if the order does not affect the result.
For example, addition is commutitive for the real numbers; thus, if $a,b$ are both real:
$a+b=b+a$
An operation that is not commutative is subtraction over the reals; ie, the following is not true:
$a-b=b-a$
# Programmed Math/Counting
## Origin of Counting

Perhaps, counting began when early men did something like put a stone in a bowl or a pit in the ground for each of his flock that went out to graze. When the flock returned he would take out a stone for each returning animal. If there was a stone or stones left after the last animal returned he would know that he needed to find out what happened to that or those animals.
It is possible that he would begin to give a name for each group of stones, that is one stone, would have a name, two stones would have a name and so-forth. It is also probable that he already had a name for numbers based on counting with fingers. Counting on fingers might have been the beginning of dividing numbers into groups of ten.

## Learning to Count

Watching a three year old learn to count there a number of apparent stages.
First they learn to repeat a series of sounds they hear "aye-bee-cee-dee..." and "one-two-three-four..."
Second they associate the sounds "one-two-three-four..." with pointing at a group of objects, but don't yet make the one to one association.
Then they start to learn the one to one association between the objects and the words.
Finally they start learning the rules needed to count accurately,
* Point at each object as you say the next word.
* Point at the object only once and move to the next.
* Don't randomly select the next object, but proceed sequentially.
* Remember where you've started and what you've already counted.

### Demonstration

Given a set of objects,
start at one side
and proceed until
each has been counted.
# Programmed Math/Measuring

Measurement in math is the act of finding the length, width, height etc... of a certain object, different measurement schemes are used for different objects.
eg:
Centimetres for small shapes, Square centimetres for area, Centimetres cubed for volume.
There are different ways of measuring geometric shapes, depending on the dimentional qualities of them. For example, measuring a line ----- long, you could count how many dashes there are, and call it 5 dashes long, or you could measure it with a ruler.
But for something like:
You would first use the formula for Area to get the inside size, or use the formula for perimeter. A=LW for a square, So Area = Length * Width
So as $4*7=28cm^{2}$
Which is 28cm squared
For perimeter in a square, you take each side and add them together. So $4+4+7+7=2*4+2*7=8+14=22$
# Programmed Math/Order of operations

Order of Operations in math is dealing with the order in which you work out an equation, which can solve many problems.
For example:
2 x 3 + 5 = x
In this example, what is x? We could either multiply 2 by 3, then add 5 to it OR we could add 3 and 5 together and multiply that by two. But how do we know?
Using BODMAS we can. BODMAS stands for Brackets Over Division Multiplication Addition Subtraction. This is the order we go in.
So using BODMAS we will multiply first and then add. So it is really:
(2x3) + 5 = x x = 11
Order of operation is also important in boolean algebra (see: Boolean Algebra). When a problem needs to be solved, it can be turned into BODMAS form to solve it. For example:
1 AND 1 OR 0 NAND 1. How would this work? If we convert it, it is:
1x1+0x1'= x
So we would go for multiplication first, 1x1 = 1.
so it is now:
1+0x1'=x
We do multiplication again: 0x1 = 0, but because this is the inverse, we make it 1.
So it is now: 1+1 = 2 (or in this case 1, because it is OR).
And our problem gets solved.
# Programmed Math/Cosine

Cosine in trigonometry is the adjacent divided hypotenuse, in the form of $\cos \theta ={\frac {a}{h}}$ An equation with Cosine would be the following when the adjacent is equal to 5 and the hypotenuse is equal to 10: $\cos \theta ={\frac {a}{h}}$ = $\cos \theta \ ={\frac {5}{10}}=.877562$
Cosine is usually used for triangle with the angle in the corner of lower point of the hypotenuse.
# Programmed Math/Rounding

Rounding is a function that deals with a sort of "evening" of numbers, to make them closer to a specific target, say a 5 or a 10, in this we say a number is nicely rounded, or round.
Here is an example:
Number a is 23.
(a): While our number remains at 23, we could either move it up (to 25) or down (to 20). Since the number is closer to 20, we make the number 20.
(b): Our number is now 26. This number is above 5. And since 30-4 =26, we will increase the number to 30, because of the small gap.
But what about the number 5? For all numbers what include 5, we round them up to the nearest 10.
(c): Number = 25. New number = 30 (after rounding).
# Programmed Math/Decimals

Decimals (or floating point numbers) are the opposite of fractions, where fractions take the form of a number over a number eg: ${\frac {1}{2}}$ which is one half.
In decimal format this would be 0.5. Why?
Well one half of 1 is 0.5 since 0.5 * 2 is equal to 1. If we multiply the number at the bottom by the decimal we should get the number at the top. Such as:
${\frac {2}{4}}$ Is still one half.
$2/4=0.5$ since ${\frac {1}{2}}={\frac {2}{4}}$ and $0.5*4=2$
So the formulae could be: ${\frac {a}{b}}=x$ and thus $x*b=a$

## Dividing Decimals

Division by decimals is similar to dividing by whole numbers.
Rebecca enjoys pushing her scooter around the City-park pond after school and on weekends. If she circles the pond 7 times and total distance of 5.88 km, what is the distance around the pond?
To divide a decimal by a whole number, divide the dividend, disregarding the decimal point. Then place the decimal point in the quotient directly above the decimal point in the dividend.

## Steps for Diving with Decimals

The problem of 8 divided 4 was easy enough. We're dealing with two whole numbers, so we just separated 8 into 4 groups to end up with 2 in each group. But what if we have decimals in our division problem? A decimal is a fraction of a whole number written as with as a number with a decimal point. 0.25 is an example of a decimal number.
# Radiation Oncology/Arrythmia

* SBRT for cardiac arrhythmias also termed stereotactic arrhythmia radioablation (STAR)
* Stereotactic radioablation has been used to safely and effectively treat a limited number of patients with malignant arrhythmias:
** Ventricular tachycardia (VT)
** Atrial fibrillation (AF)
* Unlike catheter-directed radiofrequency or cryoablation, in which tissue destruction is effected by thermal injury, radiotherapy uses gamma-rays or x-rays directed in high doses (typically 25–30 Gy) to a three-dimensional volume of target tissue
# Radiation Oncology/Authors

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Author List
* There are 34 registered users who have contributed to this wiki textbook as of August 1, 2007, and have contributed ~95% of content
* Those below have chosen to declare their personal information here
* Please feel free to add yourself to the author list, when you contribute
* Edit counts are as of July 1, 2010
Brian Cook, M.D. - Brim
    Sampson Radiation Oncology, Clinton, NC
    First authorship: September 8, 2004
    Contributions: Original concept (4478 edits, 630 pages)
Tomas Dvorak, M.D. - Tdvorak
    MD Anderson Cancer Center Orlando, Orlando, FL
    First Authorship: June 4, 2005
    Contributions: Various (8323 edits, 729 pages)
Michael Chan, M.D. - MDChanderson
    Assistant Professor of Radiation Oncology, Wake Forest University, Winston-Salem, NC
    First Authorship: July 25, 2005
    Contributions: (821 edits, 51 pages)
Andrew J. Hope, M.D. - Hope
    First authorship: February 14, 2005
    Contributions: Various (81 edits, 29 pages)
Andrew Miller, B.Med., B.Sc., Grad.Dip.Ed., FRANZCR - AAM
    Clinical Associate Professor, Illawarra Cancer Care Centre, Wollongong, Australia
    First authorship: January 2, 2005
    Contributions: Various (4 edits, 2 pages)
Cliff Robinson, M.D. - cgrobinson
    Resident, Dept. of Radiation Oncology, Cleveland Clinic Foundation, Cleveland, OH
    First Authorship: December 4, 2005
    Contributions: (3 edits, 2 pages)
Dillip Kumar Muduly, M.S. - User:Drdillipmuduly
    Resident, Dept. of Surgical Oncology, All India Institute of Medical Sciences, New Delhi, India
    First Authorship: December 4, 2012
    Contributions: (50 edits, 2 pages)
Christopher Watson, M.D. - cwatson5040
    Radiation Oncologist, Richard L. Roudebush VA Medical Center, Indianapolis, IN
    First Authorship: September 3, 2013
    Contributions: (35 edits)
Christopher Ho, M.D.（何懷德醫師）
    Taiwan Society for Therapeutic Radiology and Oncology (TASTRO，台灣放射腫瘤學會)
    First Authorship: October 4, 2019
    Contributions: (168 edits)
# Radiation Oncology/Benign

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Benign Diseases
* Trigeminal Neuralgia
* Sphenopalatine Neuralgia
* Chronic Cluster Headaches
* Acoustic neuroma (vestibular schwannoma)
* Arteriovenous malformation
* Cavernous malformation
* Hemangioma
* Graves' Disease
* Heterotopic ossification
* Ankylosing spondylitis
* Multiple sclerosis
* Pigmented Villonodular Synovitis (PVNS)
* Amyloidosis
* Fibromatosis:
** Dupuytren's Contracture
** Peyronie's Disease
** Desmoid tumors
* Heel Spurs
* Keloid
* Angiomyxoma
* Vascular Brachytherapy
* Pterygium
* Orbital pseudotumor
* Paraganglioma (Glomus tumor)
* Gynecomastia
* Rheumatoid arthritis
* Arrhythmia
* Epilepsy
* Randomized evidence
* Official guidelines (for benign diseases in general)
# Radiation Oncology/Benign/Amyloidosis

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Amyloidosis
* Characterized by deposition of insoluble protein fibers in tissues, leading to tissue dysfunction
* Usually a systemic disease with widespread protein deposition, although rare localized forms exist
Tracheobronchial Amyloidosis
# Radiation Oncology/Benign/Dupuytrens

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Dupuytren's Contracture

## Overview

* Proliferative disorder of connective tissue involving palmar fascia of the hand
* Highest prevalence in regions of Scotland, Ireland, and France
* Usually starts in 4th decade, and peaks in 5th - 6th decade
* Male: female = 3:1, with 2/3 developing bilateral disease
* Etiology and pathogenesis still poorly understood
* Clinical progression:
** Early stage: subcutaneous nodules, may be fixed to skin
** Intermediate stage: tough cords
** Late stage: cords attach to periosteum of hand bones, leading to characteristic contracture of the palm, medial phalangeal (MP) and proximal interphalangeal joints (PIP)
* Typically no invasion of muscles (unlike desmoid)
* Clinical progression in early stage disease ~50%
* Role of RT based on retrospective studies. Based on mechanism of disease, RT appears best when used early in the disease process. Randomized evidence suggests 3 Gy x 7 fractions sufficient

## Staging

Tubiana's Classification (1966)
| Stage | Description | Contracture degree |
| N | Symptoms only (nodules, skin retraction, fixation) | None |
| N/I | Symptoms + deformity | 1-10 |
| I | Symptoms + deformity | 11-45 |
| II | Symptoms + deformity | 46-90 |
| III | Symptoms + deformity | 91-135 |
| IV | Symptoms + deformity | >135 |

## Evidence

* Essen, Germany (1997-1998) -- RT 30/10 (15/5 + 15/5) vs RT 21/7
** Randomized. 129 patients, 198 involved hands. Early stage progressive disease, no surgery. Stage N (37%), Stage N/I (31%), Stage I (30%), Stage II (3%). Prophylactic RT orthovoltage, margin 1-2 cm proximal/distal and 0.5-1 cm radial. Arm 1) RT 15/5, 8 week break, 15/5 vs. Arm 2) RT 21/7. Minimum F/U 1 year
** 2001 PMID 11172962 -- "Radiotherapy optimization in early-stage Dupuytren's contracture: first results of a randomized clinical study." (Seegenschmiedt MH, Int J Radiat Oncol Biol Phys. 2001 Mar 1;49(3):785-98.)
*** Outcome: 1-year regression 56% vs 53% (NS), stable 37% vs. 38% (NS), progression 7% vs 9% (NS). Treatment "failure" 8%, but only 2% required hand surgery for progression
*** Toxicity: Acute minimal, chronic Grade 1 in 5% sites, no difference between groups
*** Conclusion: Both dose schedules equally effective to prevent disease progression. Long term F/U needed
# Radiation Oncology/Benign/Guidelines

Radiation Therapy for Benign Disease Official Guidelines
DEGRO (German Society for Radiation Oncology):
* 2014 PMID 25238992 -- "DEGRO guidelines for the radiotherapy of non-malignant disorders : Part II: Painful degenerative skeletal disorders."
* 2002 PMID 11872298 -- "Consensus guidelines for radiation therapy of benign diseases: a multicenter approach in Germany."
# Radiation Oncology/Appendix-carcinoma

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Carcinoma of the Appendix
This chapter is about carcinomas only. For carcinoid tumors of the appendix, see Carcinoid of the appendix

## Staging

Was added as a separate classification starting with the 7th edition of the AJCC Staging Manual. Previously, this was staged using the colorectal staging system.
Carcinoid tumors of the appendix are staged separately.
AJCC 7th Edition (2009) Tumor
* Tis - carcinoma in situ
* T1 - invasion of submucosa
* T2 - invasion of muscularis propria
* T3 - invasion through muscularis propria into subserosa or into mesoappendix
* T4
** T4a - penetrates visceral peritoneum, including mucinous peritoneal tumor within the right lower quadrant
** T4b - directly invades other organs or structures (includes invasion of other segments of the colorectum by way of the serosa)
Nodes
* N0 - no regional lymph node metastasis
* N1 - metastasis in 1-3 regional LN
* N2 - metastasis in 4 or more LN
Distant Metastasis
* M0 - none
* M1 - distant metastasis
** M1a - intraperitoneal metastasis beyond the right lower quadrant, including pseudomyxoma peritonei
** M1b - nonperitoneal metastasis
Stage grouping
* I - T1-2 N0
* IIA - T3 N0
* IIB - T4a N0
* IIC - T4b N0
* IIIA - T1-2 N1
* IIIB - T3-4 N1
* IIIC - N2
* IVA - M1a N0 and Grade 1
* IVB - M1a N0 and Grade 2-3, M1a and N+ (any Grade)
* IVC - M1b
# Radiation Oncology/Benign/Ankylosing spondylitis

* Front Page: Radiation Oncology | RTOG Trials | Randomized Trials
Radiation was used routinely for the treatment of AS from the 1930s through the 1950s. It has since been largely abandoned due to the concern for secondary malignancies.
Treatment can be by EBRT, Radium-224, or Samarium-153.

## Risk of malignancy

* PMID 3814487, 1987 (1935-54) — "Long term mortality after a single treatment course with X-rays in patients treated for ankylosing spondylitis." Darby SC et al. Br J Cancer. 1987 Feb;55(2):179-90.
** Mortality thru 1983 was assessed for 14,000 pts with AS treated with a single course of X-rays from 1935-54.
** 28% increase in mortality from neoplasms other than leukemia or colon cancer. 3X increase in deaths from leukemia. 30% increase in mortality from colon cancer.
# Optics/Images

There are two types of images that can be formed: Real and virtual.

## Real images

Real images are images that are formed at the same side as the either the reflected or transmitted rays. Rays actually passed through the points in the image and are being picked up by your eyes. As a result they can be focused on to a projection screen. By convention, the position of a real image is greater than zero.

## Virtual images

Virtual images are those that appear at the same side as the incident rays. Rays did not actually pass through the image but you can virtually trace the rays back to the location of the image as if the rays originated from there. Any mirror or lens can produce a virtual image. Virtual images are described by a negative image location.
# Optics/Lenses

* Holding a magnifying glass against a wall at the proper distance usually will provide a picture of the lit-up parts of the room. Note that that distance varies, depending on the distance of the object concerned from the lens. Objects that are far away will require a distance called the focal length, while objects that are closer to the lens require a longer distance for a sharp picture of that object on the wall.
* Eye glasses restore proper sight to very many people, also eyepieces of optical instruments include lenses.
* Photography has many uses
See also wikipedia: List of many optics topics

## Refraction at a spherical interface

See also wikipedia:Refraction

## A lens
### Locating the image

See also
* Photography
* Basics of the Camera
* wikipedia:Camera

### The lensmaker’s equation

See also
* Optical Instruments
* wikipedia:Lens
* wikipedia:Photographic lens

### Converging and diverging lenses

See also
* wikipedia:Convex lens
* wikipedia:Concave lens

## See also

* Physics Study Guide/Optics
* Waves/Geometrical Problems
* wikipedia: Lenses
* wikipedia:Optical devices
# Optics/Light

Visible light (commonly referred to simply as light) is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has a wavelength in the range of about 380 nanometres to about 740 nm – between the invisible infrared, with longer wavelengths and the invisible ultraviolet, with shorter wavelengths.
Primary properties of visible light are intensity, propagation direction, frequency or wavelength spectrum, and polarisation, while its speed in a vacuum, 299,792,458 meters per second (about 300,000 kilometers per second), is one of the fundamental constants of nature. Visible light, as with all types of electromagnetic radiation (EMR), is experimentally found to always move at this speed in vacuum.
In common with all types of EMR, visible light is emitted and absorbed in tiny "packets" called photons, and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important research area in modern physics.
In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not.
# Optimal Classification

Optimal classification refers to any method of classification, which inexclusively minimizes the number of queries necessary to identify a particular element within a bounded class.

## Table of Contents

Rypka's Method
* Truth Table Size-Related Equations
* Separatory Equations
** Element-Related equations
** Characteristic-related equations
*** Theoretical separation
*** Empirical separation
**** Target Set Truth Table Values
**** Separation Stages
* Computational Example
* Application Example

## Notes

* ↑ Although classification elements and attributes and decision actions and conditions may employ tables and trees there are important differences in how each is defined. A classification table or tree is defined by having an element with at least one attribute with at least one value and may have more than one element, attribute or attribute value but may not have more than one element per rule. On the other hand, a decision table or tree may have more than one condition per rule, more than one state per condition and more than one action per rule.
* ↑ A bounded class is a collection of elements defined by the same finite group of attributes.

## Specific applications

* Classification of closed legal cases to help identify new ones
* Artificial Neural Networks
** Compute minimum number of hidden nodes
** Minimize training time
* Dynamic classification of publications
* Soil taxonomy

## See also

* Data mining
* Fuzzy logic
* Information retrieval

## External links

* LIBRARY OF CONGRESS CLASSIFICATION OUTLINE
* North American Industry Classification System (NAICS)
* 2000 Mathematics Subject Classification
* Standard Industrial Classification (SIC) System Search
* U.S. Patent Classification (USPC) System
* The Classification Society of North America (CSNA)
* "What is "entropy and information gain"?, in the context of decision trees?"
# Optics/Total internal reflection

Total internal reflection is a phenomenon that occurs when light travels from a more optically dense medium (or a medium with higher refractive index ${n_{1}}$) to a less optically dense one (lower index ${n_{2}}$), such as glass to air or water to air. When light travels from an optically dense medium to a less optically dense medium, the light refracts away from the normal. If the angle of incidence is gradually increased, one will notice that at a certain point, the refracted ray deviates so far away from the normal that it reflects rather than refracts. This results whenever the refracted angle predicted by Snell's Law becomes greater than 90 degrees.
The critical angle $\theta _{c}$ is defined as the angle of incidence (inside the higher-index material) for which Snell's Law predicts a 90-degree angle of refraction -- this would mean the light follows the surface rather than entering the low-index material.
One can calculate the critical angle using Snell's Law:
$n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}\,\!$
$n_{1}\sin \theta _{c}=n_{2}\sin 90^{\circ }=n_{2}$
$\sin \theta _{c}={\frac {n_{2}}{n_{1}}}$
$\theta _{c}=\sin ^{-1}\left({\frac {n_{2}}{n_{1}}}\right)$
Total internal reflection will occur for any incident angle greater than θ$_c$.
Because the reflected ray never leaves the higher-index material, Snell's Law for total internal reflection becomes $n_{1}\sin \theta _{1}=n_{1}\sin \theta _{2}$, in other words $\theta _{1}=\theta _{2}$, which is the law of reflection.
There is always a fraction of the energy reflected at a boundary between materials of different refractive index, but it is usually quite small (typically a few percent). In the case of total internal reflection, however, 100% of the beam energy reflects (hence the name "total").
You can easily observe total internal reflection for yourself next time you are in a swimming pool. If you are under water looking up, you see the sky. As you turn your head to look closer to horizontal, you see a reflection of the bottom (or side) of the pool. These rays from the pool bottom hit the water-to-air boundary at an angle of incidence greater than the critical angle, so they are reflected to you.
How do I know that the reflected ray isn't just the refracted ray? The second law of reflection states that "the incident ray, the reflected ray, and the normal are coplanar." Therefore, the refracted ray must be in the second medium. If it is in the same medium that it originated from, then it is the reflected ray. The reflected angle is also the same as the incident angle, which agrees with the first law of reflection.
# Optics/Waves

In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium (space or mass). Frequency refers to the addition of time.
# Pinyin/Winner Is The King

《Winner is the King》
The history of human society
has cited
the theory of
"the winner is the king".
《shehngzhee-weir-warng》
rernleih shehhuih de lihshii
yiinzhehng le
"shehngzhee-weir-warng"
de daohlii.
# Pinyin/Without

See also
# Pinyin/Woman

Search Pinyin woman
A woman is an adult female human.
fuhnvv shih cherngniarn d nvvrern.
# Pinyin/Worcester sauce

Worcester sauce is a dark thin sauce that is made of vinegar, soya sauce, and spices.
Worcester sauce shì yī zhǒng yòng cù, jiàngyóu, hé xiāngliào zhìchéng de shēnsè xībó de jiàngliào.
# Pinyin/Word
## Noun

* a word is a single unit of written or spoken language.
** ciryuu shih wernzih huoh yuuyarn d danweih.
# Pinyin/Wisdom

See also
# Pinyin/With

Search with
# Pinyin/Wine

Search Pinyin wine