Geometry - Expanding the Wiki - Calvin Lin

$\color{#D61F06} { \text{ Updated! October 30} }$

I have added the new skills to the Geometry Map. I look forward to reading what you have to share :)

Thanks for your suggestions for the Algebra Map. I encourage you to check it out, and contribute to the Wiki where you can.

I am interested now building the Geometry Map beyond what is covered in high school, and it will include skills that are used in Olympiad Problem Solving. Please take a look at Upcoming Skill Maps - Geometry Extension for the (most updated) proposed extension.

I have the following questions. Please reply to the appropriate comment, to make it easy for me to track.

1) Are there any subtopics that I missed out? What else do you want to see?
2) Vectors Chapter - Anything I missed out? Please look over the Applications of dot product / cross product, and add to that.
3) Geometric Transformations - Inversion feels out of place here. Should it be placed elsewhere?
4) Euclidean Geometry - Suggestions on how to better organize this section? There are also a lot of skills missing, so please contribute
5) Coordinate Geometry - This seems complete to me.
6) Non Euclidean Geometry - This is sparse, and could use your help to build out.
7) Any other comments?

Note: To keep the discussion on topic, I will be removing irrelevant comments.

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print "hello world"

Math

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Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

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\boxed{123}

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Easy Math Editor

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

1) Are there any subtopics that I missed out? What else do you want to see?

Calvin Lin Staff - 6 years, 8 months ago

We can have Descartes Theorem related to circles. I would like to write for it.

Yash Singhal - 6 years, 8 months ago

Thanks, I've added that to the list of Euclidean Geometry Theorems.

We can have BPT (Basic Proportionality Theorem) in Similar Triangles. Also, we can have different congruency types like SSS,ASA etc.

Geometry of Complex numbers

U Z - 6 years, 7 months ago

Sorry I'm a bit late on the discussion, but since I've been helping some kids in geometry I've had to do some constructions. Is there a need for a little bit about constructions, not necessarily how to construct every geometric shape with a compass and straightedge, but maybe general info about what it is and why it's done? Thanks @Calvin Lin

Edit: never mind, I saw Aaron's post on making a new wiki, I'll do that when I find the time.

Justin Wong - 6 years, 7 months ago

I added in a section of Geometric Constructions. I look forward to seeing what you have been working on.

Calvin Lin Staff - 6 years, 7 months ago

@Calvin Lin – is there are only names of topics no information about the topic???

sakshi rathore - 5 years, 10 months ago

@Sakshi Rathore – The map has been build out. You can click on Topics - Geometry to see what is available.

Calvin Lin Staff - 5 years, 10 months ago

5) Coordinate Geometry - This seems complete to me. (Note: It is in addition to the current subtopic of coordinate geometry.)

I would like to see Conic sections in more detail. I have thought of the following subtopics that could be added.

Diametric form of circle
Parametric equation of all conics.
Equations of tangents and normals of conics

Pranshu Gaba - 6 years, 8 months ago

I think that "diametirc form" and "equation of tangent/normal" should be placed in the individual conic sections, as opposed to creating a new skill for them.

I have added Parametric Equation of conics under Parametric Equations.

@Calvin Lin – All right. I have added the "diametric form" to "circle - general equation."

I think we should include the cases of Shifting of Origin. For eg: Coordinates of a point and equation of a line with respect to the new origin other than $(0,0)$ .

We could also include Rotation of the coordinate axes in coordinate geometry, as well as Matrices.

@Pranshu Gaba – Yes, they will be fine.

4) Euclidean Geometry - Suggestions on how to better organize this section? There are also a lot of skills missing, so please contribute

3) Geometric Transformations - Inversion feels out of place here. Should it be placed elsewhere?

2) Vectors Chapter - Anything I missed out? Please look over the Applications of dot product / cross product, and add to that.

7) Any other comments?

6) Non Euclidean Geometry - This is sparse, and could use your help to build out.

Suggestion for Brilliant.org If we want to expand the wiki, a nice way to attract writers would be if Brilliant gives them some additional points for every article they do. What do you think?

Jordi Bosch - 6 years, 8 months ago

That is a good suggestion. I like recognizing the contributor of a well-written Wiki page, similar to how the community responds to great problems or notes.

We currently display a "Top editors" to show whom has been responsible for making improvements to the page, which is one way to acknowledge their effort. We are also exploring other potential approaches, like making a weekly announcement of "These are the best pages added in the past week". E.g. See Great Wiki Submissions

We will appeal towards what these top contributors like, and what is healthy for the community. I do not think that awarding additional points for every article is a good approach. It is likely that this would simply result in spammy / stub posts, where people fight to add one (or the minimum possible) character in order to attain the points awarded.

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$