What is this website? on The Wonderful World of Organic Geometry

With ToC

Mon, 01 Jan 0001 00:00:00 +0000

Caput vino delphine in tamen vias #

Cognita laeva illo fracta #

Lorem markdownum pavent auras, surgit nunc cingentibus libet Laomedonque que est. Pastor An arbor filia foedat, ne fugit aliter, per. Helicona illas et callida neptem est Oresitrophos caput, dentibus est venit. Tenet reddite famuli praesentem fortibus, quaeque vis foret si frondes gelidos gravidae circumtulit inpulit armenta nativum.

Te at cruciabere vides rubentis manebo
Maturuit in praetemptat ruborem ignara postquam habitasse
Subitarum supplevit quoque fontesque venabula spretis modo
Montis tot est mali quasque gravis
Quinquennem domus arsit ipse
Pellem turis pugnabant locavit

Natus quaerere #

Pectora et sine mulcere, coniuge dum tincta incurvae. Quis iam; est dextra Peneosque, metuis a verba, primo. Illa sed colloque suis: magno: gramen, aera excutiunt concipit.

Without ToC

Mon, 01 Jan 0001 00:00:00 +0000

At me ipso nepotibus nunc celebratior genus #

Tanto oblite #

Lorem markdownum pectora novis patenti igne sua opus aurae feras materiaque illic demersit imago et aristas questaque posset. Vomit quoque suo inhaesuro clara. Esse cumque, per referri triste. Ut exponit solisque communis in tendens vincetis agisque iamque huic bene ante vetat omina Thebae rates. Aeacus servat admonitu concidit, ad resimas vultus et rugas vultu dignamque Siphnon.

Quam iugulum regia simulacra, plus meruit humo pecorumque haesit, ab discedunt dixit: ritu pharetramque. Exul Laurenti orantem modo, per densum missisque labor manibus non colla unum, obiectat. Tu pervia collo, fessus quae Cretenque Myconon crate! Tegumenque quae invisi sudore per vocari quaque plus ventis fluidos. Nodo perque, fugisse pectora sorores.

Pascal's Theorem

Mon, 01 Jan 0001 00:00:00 +0000

Pascal’s Theorem #

Pascal’s theorem (Blaise Pascal, 1640 — the hexagrammum mysticum) states:

If six points lie on a conic, then the three pairs of opposite sides of the hexagon they form meet in three collinear points. The line containing them is the Pascal line.

It is the projective generalization of Pappus’s theorem (which is the special case where the conic degenerates into two lines), and it is dual to Brianchon’s theorem.

Everything comes in pairs

Tue, 11 Mar 2025 00:00:00 +0000

We saw in the previous tutorial that projective geometry arose out of perspective painting by the addition of new elements, first noticed by Renaissance painters, where parallel lines and planes meet.

The addition of these new elements in projective geometry (PG) had unexpected and far-reaching consequences. To simplify the discussion, we focus now on 2D projective geometry, the projective plane $P(\mathbb{R}^2)$. It arises from the euclidean plane $\mathbf{E}^2$ by adding an ideal line along with all its points, the ideal points of the projective plane.

Testing Ganja code

Tue, 11 Mar 2025 00:00:00 +0000

Testing ganja code in html #

On this page I want to test including ganja code directly in the post. This will allow me then to convert the ganja notebooks that I have created into Hugo pages.

You can drag the center of the animated circle.

TODO

Tue, 11 Mar 2025 00:00:00 +0000

TODO List #

Figure out how to organize menus
Figure out whether it’s possible to have any GO templates in md files since I’m using unsafe = true
Figure out how to get rid of borders on geogebra demos
Investigate how to add GUI to ganja demos
Look into font size and spacing – it seems small and spread out
Migrate the ganja notebooks into pgbook
Figure out how to pass parameters to the ganja scripts
Why do the floated figures have so much space below them?

Sample page

Fri, 17 Jan 2025 14:05:11 +0100

A sample page #

In this post I am checking out the capabilities that are needed for visualizing mathematics.

For example, $\LaTeX$:

\[ \begin{aligned} KL(\hat{y} || y) &= \sum_{c=1}^{M}\hat{y}_c \log{\frac{\hat{y}_c}{y_c}} \\ JS(\hat{y} || y) &= \frac{1}{2}(KL(y||\frac{y+\hat{y}}{2}) + KL(\hat{y}||\frac{y+\hat{y}}{2})) \end{aligned} \]

Interactive GeoGebra demo #

Here is a GeoGebra demo of Pascal’s theorem. You can’t access the main menu but you can use the construction tools. First we show both in a 2-column format. Unfortunately the GeoGebra borders are huge and I don’t know how to omit them.

Organic geometry

Tue, 14 Jan 2025 00:00:00 +0000

The rise of a new geometry #

Girard Desargues (1591-1661), mathematician, architect and engineer, discovered a new and intriguing geometry, which he reported on in the short book “Rough draft of an essay on the results of taking plane sections of a cone” (1639). Introducing new concepts into geometry related to the rise of perspective painting, the book provided startling new proofs of Apollonius’s classical results on conics. Desargues’ work was far ahead of its time, and vanished almost without a trace soon after his death.

(Hu)go Template Primer

Wed, 02 Apr 2014 00:00:00 +0000

Hugo uses the excellent Go html/template library for its template engine. It is an extremely lightweight engine that provides a very small amount of logic. In our experience that it is just the right amount of logic to be able to create a good static website. If you have used other template systems from different languages or frameworks you will find a lot of similarities in Go templates.

This document is a brief primer on using Go templates. The Go docs provide more details.

Getting Started with Hugo

Wed, 02 Apr 2014 00:00:00 +0000

Step 1. Install Hugo #

Go to Hugo releases and download the appropriate version for your OS and architecture.

Save it somewhere specific as we will be using it in the next step.

More complete instructions are available at Install Hugo

Step 2. Build the Docs #

Hugo has its own example site which happens to also be the documentation site you are reading right now.

Follow the following steps:

Mon, 01 Jan 0001 00:00:00 +0000

Caesorum illa tu sentit micat vestes papyriferi #

Inde aderam facti; Theseus vis de tauri illa peream. Oculos uberaque non regisque vobis cursuque, opus venit quam vulnera. Et maiora necemque, lege modo; gestanda nitidi, vero? Dum ne pectoraque testantur.

Venasque repulsa Samos qui, exspectatum eram animosque hinc, aut manes, Assyrii. Cupiens auctoribus pariter rubet, profana magni super nocens. Vos ius sibilat inpar turba visae iusto! Sedes ante dum superest extrema.

Mon, 01 Jan 0001 00:00:00 +0000

Quondam non pater est dignior ille Eurotas #

Latent te facies #

Lorem markdownum arma ignoscas vocavit quoque ille texit mandata mentis ultimus, frementes, qui in vel. Hippotades Peleus pennas conscia cuiquam Caeneus quas.

Pater demittere evincitque reddunt
Maxime adhuc pressit huc Danaas quid freta
Soror ego
Luctus linguam saxa ultroque prior Tatiumque inquit
Saepe liquitur subita superata dederat Anius sudor

Cum honorum Latona #

O fallor in sustinui iussorum equidem. Nymphae operi oris alii fronde parens dumque, in auro ait mox ingenti proxima iamdudum maius?

Mon, 01 Jan 0001 00:00:00 +0000

Buttons #

Buttons are styled links that can lead to local page or external link.

Example #

{{< button relref="/" [class="..."] >}}Get Home{{< /button >}}
{{< button href="https://github.com/alex-shpak/hugo-book" >}}Contribute{{< /button >}}

Get Home Contribute

Mon, 01 Jan 0001 00:00:00 +0000

Columns #

Columns help organize shorter pieces of content horizontally for readability.

Example #

{{% columns [ratio="1:1"] [class="..."] %}} <!-- begin columns block -->
# Left Content
Lorem markdownum insigne...

<---> <!-- magic separator, between columns -->

# Mid Content
Lorem markdownum insigne...

<---> <!-- magic separator, between columns -->

# Right Content
Lorem markdownum insigne...
{{% /columns %}}

Left Content #

Lorem markdownum insigne. Olympo signis Delphis! Retexi Nereius nova develat stringit, frustra Saturnius uteroque inter! Oculis non ritibus Telethusa protulit, sed sed aere valvis inhaesuro Pallas animam: qui quid, ignes. Miseratus fonte Ditis conubia.

Mon, 01 Jan 0001 00:00:00 +0000

Details #

Details shortcode is a helper for details html5 element. It is going to replace expand shortcode.

Example #

{{% details "Title" [open] %}}
## Markdown content
Lorem markdownum insigne...
{{% /details %}}

{{% details title="Title" open=true %}}
## Markdown content
Lorem markdownum insigne...
{{% /details %}}

Title

Markdown content #

Lorem markdownum insigne…

Mon, 01 Jan 0001 00:00:00 +0000

Hints #

Hint shortcode can be used as hint/alerts/notification block.
There are 3 colors to choose: info, warning and danger.

{{% hint [info|warning|danger] %}}
**Markdown content**  
Lorem markdownum insigne. Olympo signis Delphis! Retexi Nereius nova develat
stringit, frustra Saturnius uteroque inter! Oculis non ritibus Telethusa
{{% /hint %}}

Example #

Markdown content
Lorem markdownum insigne. Olympo signis Delphis! Retexi Nereius nova develat stringit, frustra Saturnius uteroque inter! Oculis non ritibus Telethusa

Mon, 01 Jan 0001 00:00:00 +0000

Mermaid Chart #

MermaidJS is library for generating svg charts and diagrams from text.

Override Mermaid initialization config
To override the initialization config for Mermaid, create a mermaid.json file in your assets folder!

Example #

{{< mermaid [class="..."] >}}
stateDiagram-v2
    State1: The state with a note
    note right of State1
        Important information! You can write
        notes.
    end note
    State1 --> State2
    note left of State2 : This is the note to the left.
{{< /mermaid >}}

stateDiagram-v2
    State1: The state with a note
    note right of State1
        Important information! You can write
        notes.
    end note
    State1 --> State2
    note left of State2 : This is the note to the left.

Mon, 01 Jan 0001 00:00:00 +0000

First page #

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Mon, 01 Jan 0001 00:00:00 +0000

Second Page #

Mon, 01 Jan 0001 00:00:00 +0000

Tabs #

Tabs let you organize content by context, for example installation instructions for each supported platform.

{{% tabs "id" %}}
{{% tab "MacOS" %}} # MacOS Content {{% /tab %}}
{{% tab "Linux" %}} # Linux Content {{% /tab %}}
{{% tab "Windows" %}} # Windows Content {{% /tab %}}
{{% /tabs %}}

Example #

MacOS

MacOS #

This is tab MacOS content.

What is this website? on The Wonderful World of Organic Geometry

With ToC

Caput vino delphine in tamen vias #

Cognita laeva illo fracta #

Natus quaerere #

Without ToC

At me ipso nepotibus nunc celebratior genus #

Tanto oblite #

Pascal's Theorem

Pascal’s Theorem #

Everything comes in pairs

Testing Ganja code

Testing ganja code in html #

TODO

TODO List #

Sample page

A sample page #

Interactive GeoGebra demo #

Organic geometry

The rise of a new geometry #

(Hu)go Template Primer

Getting Started with Hugo

Step 1. Install Hugo #

Step 2. Build the Docs #

4th Level of Menu #

Caesorum illa tu sentit micat vestes papyriferi #

This page is hidden in menu #

Quondam non pater est dignior ille Eurotas #

Latent te facies #

Cum honorum Latona #

Buttons #

Example #

Columns #

Example #

Left Content #

Details #

Example #

Markdown content #

Hints #

Example #

Mermaid Chart #

Example #

First page #

Second Page #

Tabs #

Example #

MacOS #