update links following renaming

_quarto.yml

@@ -9,15 +9,15 @@ website:
     left:
       - text: "Math"
         menu:
-          - ./posts/polycount/index.qmd
+          - ./posts/math/polycount/index.qmd
-          - ./posts/pentagons/index.qmd
+          - ./posts/math/pentagons/index.qmd
-          - ./posts/chebyshev/index.qmd
+          - ./posts/math/chebyshev/index.qmd
-          - ./posts/stereo/index.qmd
+          - ./posts/math/stereo/index.qmd
-          - ./posts/permutations/index.qmd
+          - ./posts/math/permutations/index.qmd
-          - ./posts/type-algebra/index.qmd
+          - ./posts/math/type-algebra/index.qmd
-          - ./posts/number-number/index.qmd
+          - ./posts/math/number-number/index.qmd
-          - ./posts/finite-field/index.qmd
+          - ./posts/math/finite-field/index.qmd
-          - ./posts/misc/index.qmd
+          - ./posts/math/misc/index.qmd
     right:
       - ./about/index.qmd
       - icon: github
@@ -32,123 +32,123 @@ website:
       contents:
         - section: "Topics"
           contents:
-            - ./posts/polycount/index.qmd
+            - ./posts/math/polycount/index.qmd
-            - ./posts/pentagons/index.qmd
+            - ./posts/math/pentagons/index.qmd
-            - ./posts/chebyshev/index.qmd
+            - ./posts/math/chebyshev/index.qmd
-            - ./posts/stereo/index.qmd
+            - ./posts/math/stereo/index.qmd
-            - ./posts/permutations/index.qmd
+            - ./posts/math/permutations/index.qmd
-            - ./posts/type-algebra/index.qmd
+            - ./posts/math/type-algebra/index.qmd
-            - ./posts/number-number/index.qmd
+            - ./posts/math/number-number/index.qmd
-            - ./posts/finite-field/index.qmd
+            - ./posts/math/finite-field/index.qmd
-            - ./posts/misc/index.qmd
+            - ./posts/math/misc/index.qmd
 
     - id: misc-sidebar
       style: "floating"
       contents:
         - section: "Miscellaneous"
           contents:
-            - ./posts/misc/platonic-volume/index.qmd
+            - ./posts/math/misc/platonic-volume/index.qmd
-            - ./posts/misc/infinitesimals/index.qmd
+            - ./posts/math/misc/infinitesimals/index.qmd
 
     - id: polycount-sidebar
       style: "floating"
       contents:
         - section: "Polynomial Counting"
-          href: ./posts/polycount/index.qmd
+          href: ./posts/math/polycount/index.qmd
           contents:
             - text: "Part 1: A primer"
-              href: ./posts/polycount/1/index.qmd
+              href: ./posts/math/polycount/1/index.qmd
             - text: "Part 2: Binary and beyond"
-              href: ./posts/polycount/2/index.qmd
+              href: ./posts/math/polycount/2/index.qmd
             - text: "Part 3: The third degree"
-              href: ./posts/polycount/3/index.qmd
+              href: ./posts/math/polycount/3/index.qmd
             - text: "Part 4: Two twos"
-              href: ./posts/polycount/4/index.qmd
+              href: ./posts/math/polycount/4/index.qmd
               contents:
               - text: "Appendix"
-                href: ./posts/polycount/4/appendix/index.qmd
+                href: ./posts/math/polycount/4/appendix/index.qmd
             - text: "Part 5: Pentamerous multiplication"
-              href: ./posts/polycount/5/index.qmd
+              href: ./posts/math/polycount/5/index.qmd
             - section: 2D
               contents:
                 - text: "Part 1: Lines, leaves, and sand"
-                  href: ./posts/polycount/sand-1/index.qmd
+                  href: ./posts/math/polycount/sand-1/index.qmd
                 - text: "Part 2: Reorienting Polynomials"
-                  href: ./posts/polycount/sand-2/index.qmd
+                  href: ./posts/math/polycount/sand-2/index.qmd
 
     - id: pentagons-sidebar
       style: "floating"
       contents:
         - section: "12 Pentagons"
-          href: ./posts/pentagons/index.qmd
+          href: ./posts/math/pentagons/index.qmd
           contents:
             - text: "Part 1"
-              href: ./posts/pentagons/1/index.qmd
+              href: ./posts/math/pentagons/1/index.qmd
             - text: "Part 2"
-              href: ./posts/pentagons/2/index.qmd
+              href: ./posts/math/pentagons/2/index.qmd
             - text: "Part 3"
-              href: ./posts/pentagons/3/index.qmd
+              href: ./posts/math/pentagons/3/index.qmd
 
     - id: chebyshev-sidebar
       style: "floating"
       contents:
         - section: "Generating Polynomials"
-          href: ./posts/chebyshev/index.qmd
+          href: ./posts/math/chebyshev/index.qmd
           contents:
             - text: "Part 1: Regular Constructability"
-              href: ./posts/chebyshev/1/index.qmd
+              href: ./posts/math/chebyshev/1/index.qmd
             - text: "Part 2: Ghostly Chains"
-              href: ./posts/chebyshev/2/index.qmd
+              href: ./posts/math/chebyshev/2/index.qmd
             - text: "Extra: Legendary"
-              href: ./posts/chebyshev/extra/index.qmd
+              href: ./posts/math/chebyshev/extra/index.qmd
 
     - id: stereography-sidebar
       style: "floating"
       contents:
         - section: "Algebraic Stereography"
-          href: ./posts/stereo/index.qmd
+          href: ./posts/math/stereo/index.qmd
           contents:
-            - ./posts/stereo/1/index.qmd
+            - ./posts/math/stereo/1/index.qmd
-            - ./posts/stereo/2/index.qmd
+            - ./posts/math/stereo/2/index.qmd
 
     - id: permutations-sidebar
       style: "floating"
       contents:
         - section: "A Game of Permutations"
-          href: ./posts/permutations/index.qmd
+          href: ./posts/math/permutations/index.qmd
           contents:
             - text: "Part 1"
-              href: ./posts/permutations/1/index.qmd
+              href: ./posts/math/permutations/1/index.qmd
             - text: "Part 2"
-              href: ./posts/permutations/2/index.qmd
+              href: ./posts/math/permutations/2/index.qmd
             - text: "Part 3"
-              href: ./posts/permutations/3/index.qmd
+              href: ./posts/math/permutations/3/index.qmd
             - text: "Appendix"
-              href: ./posts/permutations/appendix/index.qmd
+              href: ./posts/math/permutations/appendix/index.qmd
 
     - id: type-algebra-sidebar
       style: "floating"
       contents:
         - section: "Type Algebra and You"
-          href: ./posts/type-algebra/index.qmd
+          href: ./posts/math/type-algebra/index.qmd
           contents:
             - text: "Part 1: Basics"
-              href: ./posts/type-algebra/1/index.qmd
+              href: ./posts/math/type-algebra/1/index.qmd
             - text: "Part 2: A Fixer-upper"
-              href: ./posts/type-algebra/2/index.qmd
+              href: ./posts/math/type-algebra/2/index.qmd
             - text: "Part 3: Combinatorial Types"
-              href: ./posts/type-algebra/3/index.qmd
+              href: ./posts/math/type-algebra/3/index.qmd
 
     - id: number-number-sidebar
       style: "floating"
       contents:
         - section: "Numbering Numbers"
-          href: ./posts/number-number/index.qmd
+          href: ./posts/math/number-number/index.qmd
           contents:
             - text: "From 0 to ∞"
-              href: ./posts/number-number/1/index.qmd
+              href: ./posts/math/number-number/1/index.qmd
             - text: "Ordering Obliquely"
-              href: ./posts/number-number/2/index.qmd
+              href: ./posts/math/number-number/2/index.qmd
 
     - id: finite-field-sidebar
       style: "floating"
@@ -157,16 +157,16 @@ website:
           href: ./posts/finite-field/index.qmd
           contents:
             - text: "Part 1: Preliminaries"
-              href: ./posts/finite-field/1/index.qmd
+              href: ./posts/math/finite-field/1/index.qmd
             - text: "Part 2: Matrix Boogaloo"
-              href: ./posts/finite-field/2/index.qmd
+              href: ./posts/math/finite-field/2/index.qmd
               contents:
               - text: "Appendix"
-                href: ./posts/finite-field/2/extra/index.qmd
+                href: ./posts/math/finite-field/2/extra/index.qmd
             - text: "Part 3: Roll a d20"
-              href: ./posts/finite-field/2/index.qmd
+              href: ./posts/math/finite-field/2/index.qmd
             - text: "Part 5: The Power of Forgetting"
-              href: ./posts/finite-field/2/index.qmd
+              href: ./posts/math/finite-field/2/index.qmd
 
 format:
   html:

index.qmd

@@ -2,14 +2,14 @@
 title: "Posts"
 listing:
   contents:
-    - posts/polycount/*/index.*
+    - posts/math/polycount/*/index.*
-    - posts/pentagons/*/index.*
+    - posts/math/pentagons/*/index.*
-    - posts/chebyshev/*/index.*
+    - posts/math/chebyshev/*/index.*
-    - posts/stereo/*/index.*
+    - posts/math/stereo/*/index.*
-    - posts/permutations/*/index.*
+    - posts/math/permutations/*/index.*
-    - posts/type-algebra/*/index.*
+    - posts/math/type-algebra/*/index.*
-    - posts/number-number/*/index.*
+    - posts/math/number-number/*/index.*
-    - posts/finite-field/*/index.*
+    - posts/math/finite-field/*/index.*
-    - posts/misc/*/index.*
+    - posts/math/misc/*/index.*
   sort: "date desc"
 ---

interactive/p-adics/index.qmd

@@ -27,9 +27,10 @@ Each term of the series is weighted by a geometrically decreasing coefficient *c
 
 $$
 [...d_2 d_1 d_0]_p \mapsto e^{2\pi i [d_0] / p}
-  + c e^{2\pi i [d_1 d_0] / p^2}
+    + c e^{2\pi i [d_1 d_0] / p^2}
-  + c^2 e^{2\pi i [d_2 d_1 d_0] / p^2}
+    + c^2 e^{2\pi i [d_2 d_1 d_0] / p^2}
-  + ... \\
+    + ...
+  \\
   f_N(d; p) = \sum_{n = 0}^N c^n e^{2\pi i \cdot [d_{n:0}]_p / p^{n + 1}}
 $$
 

posts/math/chebyshev/1/index.qmd

@@ -38,7 +38,7 @@ from sympy.abc import z
 ```
 
 
-[Recently](/posts/misc/platonic-volume), I used coordinate-free geometry to derive
+[Recently](/posts/math/misc/platonic-volume), I used coordinate-free geometry to derive
   the volumes of the Platonic solids, a problem which was very accessible to the ancient Greeks.
 On the other hand, they found certain problems regarding which figures can be constructed via
   compass and straightedge to be very difficult. For example, they struggled with problems
@@ -742,16 +742,13 @@ My initial jumping off point for writing this article was completely different.
 However, in the process of writing, its share of the article shrank and shrank until its
   introduction was only vaguely related to what preceded it.
 But alas, the introduction via geometric constructions flows better coming off my
-  [post about the Platonic solids](/posts/misc/platonic-volume).
+  [post about the Platonic solids](/posts/math/misc/platonic-volume).
 Also, it reads better if I rely less on "if you search for this sequence of numbers"
   and more on how to interpret the definition.
 
 Consider reading [the follow-up](../2) to this post if you're interested in another way
   one can obtain the Chebyshev polynomials.
+I have since rederived the Chebyshev polynomials without the complex exponential,
+  which you can read about in [this post](/posts/math/stereo/2).
 
 Diagrams created with GeoGebra.
-
-<!--
-Update: I have since rederived the Chebyshev polynomials without the complex exponential,
-  which you can read about in [this post]().
--->

posts/math/finite-field/2/extra/index.qmd

@@ -1,5 +1,5 @@
 ---
-title: "Exploring Finite Fields, Part 2 (Extra)"
+title: "Exploring Finite Fields, Part 2 Appendix"
 description: |
   Additional notes about polynomial evaluation.
 format:
@@ -280,7 +280,7 @@ $$
 \end{gather*}
 $$
 
-The "[path swaps](/posts/permutations/1/)" shown commute only the adjacent elements.
+The "[path swaps](/posts/math/permutations/1/)" shown commute only the adjacent elements.
 By contrast, the permutation $(0 ~ 2)$ commutes *Ξ*~0~ past both *Ξ*~1~ and *Ξ*~2~.
 But since we already know *Ξ*~0~ and *Ξ*~1~ commute by the above list,
   we learn at this step that *Ξ*~0~ and *Ξ*~2~ commute.

posts/math/finite-field/3/index.qmd

@@ -281,7 +281,7 @@ If you've studied enough group theory, you know that there are two groups of ord
 Since the former group has order-6 elements, but none of these matrices are of order 6,
   the matrix group must be isomorphic to the latter.
 Since the group is small, it's not too difficult to construct an isomorphism between the two.
-Writing the elements of *S*~3~ in [cycle notation](/posts/permutations/1/), we have:
+Writing the elements of *S*~3~ in [cycle notation](/posts/math/permutations/1/), we have:
 
 $$
 \begin{gather*}

posts/math/index.qmd

@@ -2,14 +2,14 @@
 title: "Posts by topic"
 listing:
   contents:
-    - posts/polycount/index.*
+    - /posts/math/polycount/index.*
-    - posts/pentagons/index.*
+    - /posts/math/pentagons/index.*
-    - posts/chebyshev/index.*
+    - /posts/math/chebyshev/index.*
-    - posts/stereo/index.*
+    - /posts/math/stereo/index.*
-    - posts/permutations/index.*
+    - /posts/math/permutations/index.*
-    - posts/type-algebra/index.*
+    - /posts/math/type-algebra/index.*
-    - posts/number-number/index.*
+    - /posts/math/number-number/index.*
-    - posts/finite-field/index.*
+    - /posts/math/finite-field/index.*
-    - posts/misc/*/index.*
+    - /posts/math/misc/*/index.*
   sort: false
 ---

posts/math/misc/platonic-volume/index.qmd

@@ -361,7 +361,7 @@ It is half the length of the diagonal, so the ratio of a diagonal to a side is a
 
 To make calculations easier, some conversions will be made to base *φ*, or phinary.
 If you are not familiar already with phinary, I have already written at length about it [here](
-  /posts/polycount/1
+  /posts/math/polycount/1
 ).
 
 To calculate the apothem, we can calculate the sagitta *s* and height *l* by similar triangles.

posts/math/number-number/1/index.qmd

@@ -689,7 +689,7 @@ Personally, I like this definition a bit better, if only because it matches othe
 For example,
 
 - In topology, it's common to show that this interval is homeomorphic to the entire real line
-- It's similar to the [rational functions which appear in stereography](/posts/stereo/1/),
+- It's similar to the [rational functions which appear in stereography](/posts/math/stereo/1/),
   which continue to infinity instead of being periodic
 - It showcases how the Stern-Brocot tree sorts rational numbers by complexity better
 

posts/math/permutations/3/index.qmd

@@ -89,7 +89,7 @@ At least our beloved paths are left untouched, since $L(P_n) = P_{n-1}$.
 ### Coxeter Diagrams
 
 As it turns out, these restrictions are significant and produce some very deep mathematical objects,
-  known as *Coxeter diagrams* (named for the same Coxeter as in [Goldberg-Coxeter](/posts/pentagons/1)).
+  known as *Coxeter diagrams* (named for the same Coxeter as in [Goldberg-Coxeter](/posts/math/pentagons/1)).
 In this domain, the aforementioned rules about vertices and edges apply:
   each vertex corresponds to an order 2 element and each edge signifies
   that the product of two elements has order 3.

posts/math/polycount/4/appendix/index.qmd

@@ -234,7 +234,7 @@ In fact, since the expansions are in binary or (balanced) ternary, the integers
   be a subset of the 2-adics or 3-adics.
 
 Still, I wanted to see what these numbers actually "look" like, so I whipped up an interactive diagram.
-You should definitely see [this page](/interactive/adic/) for more information, but
+You should definitely see [this page](/interactive/p-adics/) for more information, but
   the gist is that *p*-adics can be sent into the complex plane in a fractal-like way.
 
 

posts/math/polycount/4/appendix/showAdicWithKappa.ojs

@@ -18,7 +18,7 @@ adicExpansionsQuotRem = FileAttachment(
   "./cendree_QuotRem_count_1024_256_digits.csv"
 ).text().then(asIntegers);
 
-import { expansions as oldExpansions } with { base as base } from "../../../../interactive/p-adics/showAdic.ojs";
+import { expansions as oldExpansions } with { base as base } from "/interactive/p-adics/showAdic.ojs";
 
 expansionsOrAdics = baseSelector == "b-adic"
   ? oldExpansions
@@ -32,7 +32,7 @@ import { plot } with {
   expansionsOrAdics as expansions,
   embedBase as embedBase,
   geometric as geometric,
-} from "../../../../interactive/p-adics/showAdic.ojs";
+} from "/interactive/p-adics/showAdic.ojs";
 
 viewof baseSelector = Inputs.radio([
   "b-adic",

posts/math/stereo/2/index.qmd

@@ -60,7 +60,7 @@ In an effort to document more interesting facts about this mathematical object
 Chebyshev Polynomials
 ---------------------
 
-[Previously](/posts/chebyshev/1), I derived the
+[Previously](/posts/math/chebyshev/1), I derived the
   [Chebyshev polynomials](https://en.wikipedia.org/wiki/Chebyshev_polynomials)
   with the archetypal complex exponential.
 These polynomials express the sines and cosines of a multiple of an angle from
@@ -99,7 +99,7 @@ Presented this way with such a simple derivation, it appears as though these rel
   are inherently trigonometric.
 
 However, these polynomials actually have *nothing* to do with sine and cosine on their own.
-For one, [they appear in graph theory](/posts/chebyshev/2), and for two,
+For one, [they appear in graph theory](/posts/math/chebyshev/2), and for two,
   the importance of the complex exponential is overstated.
 $e^{i\theta}$ really just specifies a point on the complex unit circle.
 This property is used on the second line to coax the equation into a quadratic in $e^{i\theta}$.