Merge pull request #35 from markusdemedeiros/main

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4 files changed, 32 insertions, 0 deletions

diff --git a/entries/markusde/collatz/collatz.pdf b/entries/markusde/collatz/collatz.pdf
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+++ b/entries/markusde/collatz/collatz.pdf
diff --git a/entries/markusde/collatz/collatz.png b/entries/markusde/collatz/collatz.png
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diff --git a/entries/markusde/collatz/collatz.tex b/entries/markusde/collatz/collatz.tex
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@@ -0,0 +1,21 @@
+\documentclass[12pt]{article}
+\usepackage[landscape]{geometry}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\renewcommand{\phi}{\varphi}
+\begin{document}
+
+\noindent The least fixed point of 
+\begin{align*}
+    h & : (\mathbb{N}_\bot \to \mathbb{Z}_\bot) \to (\mathbb{N}_\bot \to \mathbb{Z}_\bot) \\
+    h(F)(n) & = 
+    \begin{cases}
+        1 & n = 1 \\
+        (\phi^{n/2} + (-\phi)^{-n/2})\, F_{n/2} & n \textrm{ is even} \\
+        \sqrt[3]{\frac{\phi^{3n+1}-\phi F_{3n+1}}{10} + \frac{\sqrt{25 \phi^{3n+1} - 25\phi F_{3n+1} - 20}}{50}} + \sqrt[3]{\frac{\phi^{3n+1}-\phi F_{3n+1}}{10} - \frac{\sqrt{25 \phi^{3n+1} - 25\phi F_{3n+1} - 20}}{50}} & \textrm{otherwise} \\
+    \end{cases}
+\end{align*}
+is the Fibonacci sequence if and only if the Collatz conjecture is true.
+
+\end{document}
diff --git a/people.json b/people.json
index 2eff422..112f116 100644
--- a/people.json
+++ b/people.json
@@ -329,5 +329,16 @@
                 "link": "./entries/dewert99/fib.rs"
             }
         ]
+    },
+    {
+        "github": "markusdemedeiros",
+        "name": "Markus de Medeiros",
+        "title": "BSc Student, UBC",
+        "entries": [
+            {
+                "name": "collatz",
+                "link": "./entries/markusde/collatz/collatz.png"
+            }
+        ]
     }
 ]