OpenLLM-France/wikimedia huggingface dataset:
# Korean/Words/누나

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 누나
### Noun

* 같은 부모에게서 태어난 사이거나 일가친척 가운데 항렬이 같은 사이에서, 남자가 손위 여자를 이르거나 부르는 말. 때로는 남남끼리 나이가 적은 남자가 손위 여자를 정답게 이르거나 부르는 말. 예: 옆집 누나.
    older sister of a male (by extension applied to close, friendly older females)

### Relatives

* 누이 (nui, "younger sister of a male")
* 언니 (eonni, "older sister of a female")

### Comparatives

| Germanic | Norse | Others |
| non #Dutch nun #English Nonne #German | nonne #Danish nunna #Faroese nonne #Norway nunna #Swedish | nunn #Estonian nunna #Finnish nuna #Slovene |
* ↑ Benedictine nuns of the Mariendonk Abbey, Grefath, Düsseldorf, Germany.
* ↑ What a coincidence it is that all wear glasses!
* ↑ https://ko.dict.naver.com/#/search?query=누나
* ↑ https://en.wiktionary.org/wiki/누나
* ↑ Synonyms: zuster #Dutch
* ↑ Synonyms: sister #English
* ↑ https://www.websters1913.com/words/Nun Nun (?), n. [OE. nunne, AS. nunne, fr. L. nonna nun, nonnus monk; cf. Gr. ?, ?; of unknown origin. Cf. Nunnery.]
* ↑ Synonyms: Schwester #German
# Korean/Words/내

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 내
### Noun

* 시내보다는 크지만 강보다는 작은 물줄기.
    river, a flowing body of water.
* 시냇물 (작사: 이종구)
* 냇물아 흘러 흘러 어디로 가니
* 강물 따라 가고 싶어 강으로 간다
* 강물아 흘러 흘러 어디로 가니
* 넓은 세상 보고 싶어 바다로 간다

### Synonyms

* 냇물 (naet-mul)
* 시내 (sinae)
* 시냇물 (sinaaet-mul)
* 강 (江, gang)
* 강물 (江물, gang-mul)

### Compounds

* 미리내 (miri-nae, "Milky Way")

### Relatives

* 미르 (mireu, "dragon")
* 물 (mul, "water; body of water")

### Comparatives

| Danube #Translation | Seine #Translations | Rhine #Translations |
| Slavic, etc. Aromanian: Duna Azerbaijani: Dunay Belarusian: Дуна́й (Dunáj) Czech: Dunaj Hungarian: Duna Polish: Dunaj Russian: Дуна́й (Dunáj) Slovak: Dunaj Sorbian: Dunaj Turkush: Tuna Ukrainian: Дуна́й (Dunáj) | Latinic Catalan: Sena French: Seine Italian: Senna Occitan: Sèina Portuguese: Sena Spanish: Sena Others Czech: Seina Dutch: Seine English: Seine German: Seine Hungarian: Szajna Russian: Се́на (Séna) | Slavic, etc. Hungarian: Rajna Latvian: Reina Lithuanian: Reinas Macedonian: Ра́јна (Rájna) Serbo-Croatian: Рајна (Rajna) |
* ↑ https://ko.dict.naver.com/#/search?query=내
* ↑ https://en.wiktionary.org/wiki/내
# Korean/Words/노

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 노
### Noun

* 물을 헤쳐 배를 나아가게 하는 기구.
    oar

### Idioms

* 노를 젓다 (no-reul jeotda, lit. "to row the oar")

### Relatives

* 키 (ki, "rudder")

### Comparatives

| oar #Translations | row #Translations |
| Nordic Old Norse: ár Danish: åre Faroese: ár Icelandic: ár Norwegian: åre Swedish: åra Germanic Dutch: riem English: oar German: Ruder | Nordic Old Norse: róa Danish: ro Faroese: rógva Icelandic: róa Norwegian: ro Swedish: ro Germanic Dutch: roeien English: row German: rudern |
* ↑ https://ko.dict.naver.com/#/search?query=노
* ↑ https://en.wiktionary.org/wiki/노
* ↑ The oar is to row.
* ↑ English oar and row may be practically a metathesis, hence cognates. From Korean perspective, it seems to begin with 로 (櫓, ro, "oar") and end with 요 (搖, yo, "to row"), hence 搖櫓 "to scull."
# Hilbert-Kunz theory/Two-dimensional graded/Relative situation/Section
## Theorem

Let
    $C\longrightarrow \operatorname {Spec} {\left(\mathbb {Z} _{g}\right)}$
be a smooth projective relative curve and let ${\mathcal {T}}$ be a vector bundle over $C$. For the generic fiber $C_{0}$ let
    $\mu _{HK}({\mathcal {T}}_{0})=\sum _{\ell }r_{\ell }\mu _{\ell }^{2}\,,$
where the $\mu _{\ell }$ are the slopes (and $r_{\ell }$ the ranks) in the Harder-Narasimhan filtration of ${\mathcal {T}}_{0}$, and for every prime number let
    ${\bar {\mu }}_{HK}({\mathcal {T}}_{p})={\frac {\sum _{k}r_{k}\mu _{k}^{2}}{p^{e}}}\,,$
where the $\mu _{k}$ are the slopes in the strong Harder-Narasimhan filtration of $F^{e*}({\mathcal {T}}_{p})$ on the fiber $C_{p}$. Then
    $\lim _{p\rightarrow \infty }{\bar {\mu }}_{HK}({\mathcal {T}}_{p})=\mu _{HK}({\mathcal {T}}_{0})\,$
In charcteristic zero and a given homogeneous ideal, we use the slopes from the Harder-Narasimhan filtration of the syzygy bundle to define the Hilbert-Kunz multiplicity by
    $e_{HK}^{0}(I)={\frac {1}{2\operatorname {deg} \,C}}{\left(\mu _{HK}(\operatorname {Syz} )-(\operatorname {deg} \,C)^{2}\sum _{i=1}^{n}d_{i}^{2}\right)}\,.$
In the relative situation, an ideal gives a syzygy bundle over the relative curve and there we can compare the slopes coming from a strong Harder-Narasimhan filtration in the fibers to get the following Corollary.

## Corollary

Let $\mathbb {Z} \subseteq S$ be a finitely generated graded domain of relative dimension two with normal fibers and let $I\subseteq S$ be a homogeneous ideal such that $I_{p}$ is an $(S\otimes _{\mathbb {Z} }\mathbb {Z} /(p))_{+}$-primary ideal for all prime reductions. Then the limit
    $\lim _{p\rightarrow \infty }e_{HK}(I_{p})$
$e_{HK}^{0}(I_{0})$
It is also known by a result of Brenner, Li, Miller, that it is enough to compute in every positive characteristic $p$ just the first Frobenius pull-back (not all Frobenius powers) and then let $p$ go to infinity to get the same limit.

## Example

The Fermat quartic $x^{4}+y^{4}+z^{4}=0$ is the easiest example where the Hilbert-Kunz multiplicity of the maximal ideal $(x,y,z)$ fluctuates with the characteristic. We have
    $e_{HK}(R_{p})={\begin{cases}3{\text{ for }}p=\pm 1\,\operatorname {mod} \,8\\3+{\frac {1}{p^{2}}}{\text{ for }}p=\pm 3\,\operatorname {mod} \,8\,.\end{cases}}\,$
The limit is of course $3$, which corresponds to the fact that the syzygy bundle is semistable in characteristic zero. The syzygy bundle is semistable for all prime characteristics $p\geq 3$, but not strongly semistable for the prime numbers $p=\pm 3\,\operatorname {mod} \,8$.
# Hilbert-Kunz theory/Invariant theory/Section

Let $G$ be a finite group acting linearly on a polynomial ring $B=K[x_{1},\ldots ,x_{n}]$ with invariant ring $A=B^{G}$. This is a positively graded $K$-algebra with irrelevant ideal $A_{+}$ consisting of all invariant polynomials of positive degree. The extended ideal ${\mathfrak {h}}=A_{+}B$ is called the Hilbert ideal. The residue class ring
    $B_{G}=B/A_{+}B\,$
is called the ring of coinvariants.
We are interested in the Hilbert-Kunz multiplicity of $A$ and of its localization at the irrelevant ideal. A result of Watanabe and Yoshida implies the following observation. It uses the fact that for regular rings the Hilbert-Kunz multiplicity of an ideal is just the colength.

## Lemma

Let $G$ be a finite group acting linearly on a polynomial ring $B=K[x_{1},\ldots ,x_{n}]$ with invariant ring $A=B^{G}$ and let ${\mathfrak {h}}=A_{+}B$ be the Hilbert ideal in $B$. Let $R$ be the localization of $A$ at the irrelevant ideal. If $K$ has positive characteristic, then
    $e_{HK}(R)={\frac {\operatorname {dim} _{K}\,(B/{\mathfrak {h}})}{\#\left(G\right)}}\,.$
With this observation we can give a Hilbert-Kunz proof of the following theorem of invariant theory (which was proved in positive characteristic by Larry Smith).

## Corollary

Let $G$ be a finite group acting linearly on a polynomial ring $B=K[x_{1},\ldots ,x_{n}]$ with invariant ring $A=B^{G}$ and let ${\mathfrak {h}}=A_{+}B$ be the Hilbert ideal. If $K$ has positive characteristic, then the invariant ring is a polynomial ring if and only if we have
    $\operatorname {dim} _{K}\,B/{\mathfrak {h}}={\#\left(G\right)}\,.$
# Euphonium/Jechasteen/Lesson 2
## First Notes

Now that you know how to form your embouchure and how to control your breath, we will start to learn how to put that learning into practice. First, let's learn a note and how to play it.
In bass clef, this is a F and is fingered using the open fingering (no valves pressed). To play this note, first play it on a piano and match the pitch with your voice and then attempt matching that pitch with your instrument.
# Euler diagram

An Euler diagram is a diagram of sets, that typically shows only non-empty intersections.
For a range of examples see Studies of Euler diagrams.
# Euphonium

The euphonium is a conical-bore, tenor-voiced brass instrument. It derives its name from the Greek word euphonion, meaning "beautiful-sounding" or "sweet-voiced" ("eu" means "well" (understood as "good" or "pleasant") and "phonium" means "voice"). The euphonium is a valved instrument, and nearly all models are piston valved, though German rotary valved models do exist (e.g. Miraphone).
The euphonium has a fundamental pitch (all valves open) of Bb, but sounds in the key of C (relative to the piano). The technique involved in playing the euphonium is quite similar to that of the trumpet, in that they fingerings and partials are more or less the same—disregarding register and transposition. However, the embouchure is much more comparable to a trombone embouchure and oftentimes the mouthpieces are used interchangeably. In the United States, the Bass Clef is generally accepted as the norm, while in Europe it is much more common to read music in Bb Treble Clef (as is written for the trumpet).

### Instructor: Jonathan Chasteen

If you are not already acquainted with elementary musical notation, please review the Wikipedia page on Music Notation. I will not be going over certain things, e.g. the basics of musical notation, so it will behoove you to know at least the elements of the musical staff. Lesson 1 - Embouchure and breath Lesson 2 - First notes

## Links

* Euphonium on Wikipedia
# Google/Search and Wikiversity/2017/Index status

* Google/Search and Wikiversity/2015/Queries contains raw data or machine-readable data. Please do not edit.
* You are encouraged to modify the descriptive header and/or footer, but please do not edit the data within Google/Search and Wikiversity/2015/Queries. You are invited to discuss the topic and/or copy the contents to a new page where anyone may participate.
# Google/Search and Wikiversity/2015/External links

* Google/Search and Wikiversity/2015/External links contains raw data or machine-readable data. Please do not edit.
* You are encouraged to modify the descriptive header and/or footer, but please do not edit the data within Google/Search and Wikiversity/2015/External links. You are invited to discuss the topic and/or copy the contents to a new page where anyone may participate.
Google Webmaster Tools en-wikiversity-org-wiki_20151231T172346Z_ExternalLinks_LinkedPages.csv
# Google/Search and Wikiversity/2015/Queries

* Google/Search and Wikiversity/2015/Queries contains raw data or machine-readable data. Please do not edit.
* You are encouraged to modify the descriptive header and/or footer, but please do not edit the data within Google/Search and Wikiversity/2015/Queries. You are invited to discuss the topic and/or copy the contents to a new page where anyone may participate.
Google Webmaster Tools en-wikiversity-org-wiki_20151231T175248Z_SearchAnalytics.csv
# Google/Search

How does Google index websites and present search results? See Google Basics for an overview.
This learning project will explore the many factors that determine how people find the information that they are looking for when they do a Google search. It will use searching of Wikiversity as an example.
Project pages:
# Google/Search and Wikiversity/2015

This is a report on some of the results found in the Dec. 31, 2015 data download with commentary. See the summary at Google/Search and Wikiversity for context. The raw data is available in the subpages below. Special:Prefixindex/Google/Search and Wikiversity/2015/

## Results from Google Webmaster Tools
### Which pages at Wikiversity are most linked to?

Overall there are very few external links to our content. As in 2009 there are numerous links from a site called wikiwix.com, but the overall number has decreased quite a bit.
The complete data can be found at Google/Search and Wikiversity/2015/External links

### Which search queries return Wikiversity pages?

In the past month Wikiversity has made between 75 to 175 "impressions" per day, with 0 to 10 clicks through to our site.
The complete data can be found at Google/Search and Wikiversity/2015/Queries
# Google/Search and Wikiversity/2017

This is a report on some of the results found in the Jan. 8, 2018 data download with commentary. See the summary at Google/Search and Wikiversity for context. The raw data is available in the subpages below. Special:Prefixindex/Google/Search and Wikiversity/2017/

## Results from Google Webmaster Tools
### Which pages at Wikiversity are most linked to?

The complete dataset is listed below. The source domain for the one entry is wikiversity.org so it looks like Google has stopped tracking external links to our site.

### Which search queries return Wikiversity pages?

In the past month Wikiversity has made between 4 to 45 "impressions" with 0 to 1 clicks through to our site.
The complete data can be found at Google/Search and Wikiversity/2017/Queries
# Google/Search and Wikiversity/2017/Queries

* Google/Search and Wikiversity/2015/Queries contains raw data or machine-readable data. Please do not edit.
* You are encouraged to modify the descriptive header and/or footer, but please do not edit the data within Google/Search and Wikiversity/2015/Queries. You are invited to discuss the topic and/or copy the contents to a new page where anyone may participate.
Google Webmaster Tools en-wikiversity-org-wiki_20180108T145330Z_SearchAnalytics.csv
# Literature/1991

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Literature/1991/Berners-Lee $^{[^]}$
* Literature/1991/Brown $^{[^]}$
* Literature/1991/Bruner $^{[^]}$
* Buckland, Michael (1991). "Information as Thing." Journal of the American Society for Information Science 42 (5): 351-360. $^{[^]}$
* Literature/1991/Callinicos $^{[^]}$
* Literature/1991/Garcia $^{[^]}$
* Literature/1991/Gray $^{[^]}$
* Literature/1991/Hayakawa $^{[^]}$
* Literature/1991/Lanigan $^{[^]}$
* Literature/1991/Lave $^{[^]}$
* Literature/1991/McCahill $^{[^]}$
* Literature/1991/Nonaka $^{[^]}$
* Literature/1991/Paul $^{[^]}$
* Literature/1991/Scientific $^{[^]}$
* Literature/1991/Simon $^{[^]}$
* Traue, James Edward (1991). Committed to Print: Selected Essays in Praise of the Common Culture of the Book. Victoria University Press. $^{[^]}$
# Literature/1991/Buckland

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Author

* Buckland was 1998 President of w: ASIS&T.

## Excerpts

* Summary : Numerous definitions have been proposed for "information". One important use of "information" is to denote knowledge imparted; another is the denote the process of informing. Some leading theorists have dismissed the attributive use of "information" to refer to things that are informative. However, "information-as-thing" deserves careful examination, partly because it is the only form of information with which information systems can deal directly. People are informed not only by intentional communications, but by a wide variety of objects and events. Being "informative" is situational and it would be rash to state of any thing that it might not be informative, hence information, in some conceivable situation. Varieties of "information-as-thing" vary in their physical characteristics and so are not equally suited for storage and retrieval. There is, however, considerable scope for using representations instead.
* Whatever information storage and retrieval systems store and retrieve is necessarily "information-as-thing".
# HGR

HGR stands for Hirschfeld–Gebelein–Rényi maximum correlation. It is a correlation metric in statistics. Compared with commonly-used Pearson's correlation coefficient, it has the advantage to handle non-linear statistical dependency. The benefit for such generalization comes with computational cost. While correlation coefficient can be computed by definition, HGR maximum correlation should be approximated by ACE ( Alternating Conditional Expectations) algorithm. The application of HGR and its extension has been found in the field of information theory, machine learning and so on.

## History

HGR maximum correlation is independently proposed by three mathematicians in 20th century. Hans proposed that the correlation can be computed by series expansion, which is not efficient and replaced by ACE latterly.

## Mathematical Description

Let X and Y be random variables, f and g be smooth transformation of X, Y respectively, HGR is defined as
    $\rho =\mathop {\max _{\mathbb {E} [f(X)]=0,\mathbb {E} [g(Y)]=0}} _{{\textrm {Var}}[f(X)]=1,{\textrm {Var}}[g(Y)]=1}\mathbb {E} [f(X)g(Y)]$

## Applications
### Information Theory

The connection between HGR and other information-theoretic metric is discussed thoroughly with local assumption.
# HDL Coding Guidelines

Coding of circuit behaviour and architecture is one of the most critical steps in the whole chip development project. It has a major impact on logic synthesis, routing results, timing robustness, verifiability and testability. The HDL Coding Guidelines help chip and macro developers/teams to rapidly understand each other's code. Macro based designs integrate easier if these common coding styles are followed. This also applies to externally developed softcores. Codes will not need modification if simulator, synthesis tool, or technology is exchanged. Code invariants with respect to Synthesis tool is given in case of a similar HDL synthesis subset. Code invariants with respect to technology is given in case of similar performance and cell set. In addition, the given guidelines enable high synthesis quality and simulation performance.
The HDL Coding Guidelines need continuous adaptation according to new tool properties and new upcoming methodologies. Please participate in this process with your design know-how. Contribute rules for HDL coding that turned out to prevent errors in the downstream flow, or recommendations that alleviate further design, re-use or maintenance.
The HDL Coding Guidelines may be passed to sub-contractors or cooperation partners. Ideally their coding works should comply to these guidelines, enabling rapid and safe integration with internally developed modules.
Reading of the HDL Coding Guidelines is most efficient at the beginning of a chip-design-project. Furthermore a code review should be considered in a very early phase of HDL coding.

## External Links

* Delay Modelling & Coding Guidelines
* Good Verilog Coding Guidelines
# HEAR in Cincinnati

Hearing health providers and researchers in the Cincinnati area came together to create HEAR in Cincinnati in 2016. Organizers included persons from each of the major hearing provider agencies in the greater Cincinnati area. The group hosted its first regional conference in January 2017. The disciplines and specialties of participating individuals included professional education, audiology, vestibular disorurrrrrrders, basic and applied research, hearing aid dispensing practices, otolaryngology, and occupational health.
Mission Statement: HEAR in Cincinnati was established to communicate, share, and collaborate on research endeavors in the greater Cincinnati area, to promote excellence in provision of services and to advance professional education.
Vision Statement: HEAR in Cincinnati will become the model program to promote collaborative research, advance education, share ideas, and identify sources of funding to support research in areas of the ear and hearing.
Conferences and outreach campaigns are held periodically.

## Participant Institutions

Cincinnati Children's Hospital
* Division of Audiology (https://www.cincinnatichildrens.org/service/a/audiology)
* Division of Developmental and Behavioral Pediatrics
* Division of Pediatric Otolaryngology
National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention
University of Cincinnati College of Allied Health Sciences, Department of Communication Sciences and Disorders
University of Cincinnati College of Medicine
* Department of Otolaryngology-Head and Neck Surgery
* Department of Audiology

## Conferences

Starting in 2017, annual conferences are held at the University of Cincinnati Medical Center.

## Outreach activities

* Free hearing screenings were offered at the Monford Height Branch Library, in Cincinnati, OH on March 3rd, 2019, in celebration of World Hearing Day.
* Wikipedia:Meetup/Cincinnati/NIOSH 2019. This hands-on event was held on February 22nd 2019, and it was designed to celebrate World Hearing Day 2019, by improving Wikipedia content related to hearing, hearing health services, hearing testing, preventive and treatment interventions. Participants were also encouraged to translate pages from the English Wikipedia into other languages. Contributions were highlighted in the World Hearing Day 2019 report of activities.
* 5k Run/Walk for Better Hearing, held on August 24th, 2019 in Cincinnati, organized by the University of Cincinnati Student Academy of Cincinnati.
# Ideas in Geometry/Center of Triangles

By: Charmaine Ramos (cramos2)
# Ideas in Geometry/Constructible Numbers

This lesson was based around Group Project 8 that we did in class on November 8th.
The packet began by introducing the idea of constructible numbers, it said
“Given a unit of measure (like inches or meters or miles), what distances can we precisely construct using a compass and straightedge? These distances are what we call constructible numbers.”
Then the packet had us create a number line when we were given the distance between 0 and 1.
To do this you should set your compass so that one leg of the compass was touching point 0 and the other leg was touching point 1. This was the distance. Then you should place the non-pencil leg on point 1 and swing the pencil side around to mark the point that was the same distance from 0 to 1 on the right of point 1. This created point 2. This is what the number line looks like now:
You could use this to create the next consecutive point for infinity.
This technique can also be used to create negative points on the number line. If the same distance measure was kept on the compass, the non-pencil leg could be placed on 0 and the pencil leg could be swung to the left to find the point -1. This is what the number line looks like now:
This could also be continued to negative infinity.
Next you are given two segments (a and b) and are asked to have them add together and subtract.
To add segments a and b together you should first draw a straight line using your straightedge. Mark an arbitrary point on the lawn you have drawn. This will be the left end point of the new segment you are creating. Then set the compass to length a. Place the non-pencil leg on the point on the line and swing the pencil leg to find the other endpoint of segment a.
Then set your compass to the length of b. Place the non-pencil leg on the right endpoint of segment a on the line you have drawn and swing the pencil side the mark the other endpoint of segment b. You have now created segment a+b.
To create a-b you must once again draw a line with your straightedge and mark a point to be the left end of segment a. Then set your compass to distance a. Place the non-pencil side on the point you have marked and swing it so that the pencil leg marks the other end of a.
Then set your compass to segment b. Place the non-pencil leg of the compass on the right endpoint of a and swing it to mark the left endpoint of b. The part of a that is not also encompassed in b is a-b.
Next you learn to create fractions by using the concept of similar triangles. Similar triangles are triangles that have the same angle measures and whose sides are proportional. This can be done using the following example:
You are given segments a and b, how can you construct a line segment of length a/b. This can be done be creating a right triangle where a is the vertical leg and b is the horizontal leg.
Now add a point that is 1 away from the right angle and create a triangle so that the vertical side is of length a/b. It is of side length a/b because the side lengths are proportional.
The main goal of this lesson was to introduce the idea of constructible numbers and how they can be created.