Knowledge garden styleguide

This note is a scratchpad for formatting conventions that make the vault readable in Obsidian and reusable in coursework/report writing.

Equations

Use display math for equations that deserve visual attention:

f = \left( rac{c \pm v_r}{c \pm v_s} ight) f_0

Immediately define every symbol after the equation. Do not assume future-Andrew remembers whether $v_{s}$ is positive toward or away from the receiver.

Units

Prefer explicit SI forms:

f = 800 Hz = 800 s^{-1}
speed of sound ≈ 300 m s^{-1}

For compound units, use a space or \, between unit factors in LaTeX, e.g. m\,s^{-1}.

Code snippets

Use fenced code blocks with a language label:

def prod(a, b):
    return a * b

Keep snippets minimal: one concept per snippet, no giant pasted programs unless the note is specifically about the program.

Diagrams

TikZ or SVG diagrams are best when they explain structure: task graphs, coordinate systems, vector components, or data pipelines. Put a one-sentence interpretation under the diagram so the image is not floating context-free.

f = 800 Hz = 800 $s^{- 1}$ Speed of sound = 300 $m s^{- 1}$

f = (\frac{c \pm v _{r}}{c \pm v _{s}}) f_{0}

where:

$f$ is observed frequency by receiver ( $r r r$ )
$c$ is the propagation speed of waves being measured
$v_{r}$ is the velocity of the r, $+ v e$ if moving towards source, $- v e$ if moving away from source
$v_{s}$ is the velocity of the source, $+ v e$ if moving away from receiver, $- v e$ if moving towards receiver
$f_{0}$ is the actual emitted frequency from the source

\require p h y s i cs \eval x_{0}^{\infty}

def prod(a, b):
	return a * b;
	
print(prod(4, 7))

\usepackage{pgfplots}% loads also tikz
\pgfplotsset{compat=newest}% to avoid the pgfplots warning
\usetikzlibrary{intersections, pgfplots.fillbetween}
\pgfdeclarelayer{pre main}
\begin{document}
\begin{tikzpicture}[scale=0.4]
 
\pgfsetlayers{pre main,main}
\tikzset{partial ellipse/.style args={#1:#2:#3}{ insert path={+ (#1:#3) arc (#1:#2:#3)} } }
\draw[name path=A, shift={(5,8)}, partial ellipse=180:360:6cm and 1.5cm];
\draw[name path=B, shift={(5,0)}, partial ellipse=180:360:6cm and 1.5cm];
\tikzfillbetween[of=A and B]{blue, opacity=0.1};
\end{tikzpicture}
\end{document}

Axiom

axm

Definition

def

Lemma

lem

Proposition

prp

Theorem

thm

Corollary

cor

Claim

clm

Assumption

asm

Exm

exm

lol

exr

Conjecture

cnj

Hypothesis

hyp

Remark

rmk

Tip

tip

Abstract

abstract

Info

info

\usetikzlibrary{arrows,decorations.pathmorphing}
\def\english#1{\emph{#1}}
\tikzset{
  arrow/.style={-stealth', line width=0.5pt},
  every picture/.append style={line width=1pt},
}
\begin{document}
\begin{tikzpicture}[
    scale=1.3,
    fib housing horz/.style={top color=black!10, bottom color=black!40, draw=black!50},
    fib housing vert/.style={left color=black!10, right color=black!40, draw=black!50},
    fib housing/.style={fill=black!20, draw=black!50},
    fib background vert/.style={left color=black!40, right color=black!10, draw=black!50},
    fib background/.style={fill=black!30, draw=black!50},
    fib lens thick/.style={draw=black!80, line width=0.04cm},
    fib lens thinn/.style={draw=black!95, line width=0.02cm},
    fib mirror/.style={draw=black!60, line width=0.03cm, fill=black!20},
    fib objective/.style={draw=black!60, line width=0.03cm},
    fib quadrupole/.style={draw=black!60, line width=0.03cm},
    fib blanker/.style={draw=black!90, fill=black!60},
    fib octopole/.style={draw=black!80, line width=0.04cm},
  ]
  % Picture created and copyright by Clemens Helfmeier in 2009 for master thesis.
  % Contact me at: Clemens@Helfmeier.de
  % Aufbau des FIBs
  % "falsch" herum, Probe unten, Ionen oben
  % einzelne Elemente sind rund, insofern auch shading anbringen
  % jedes element ist 1.4cm hoch.
  % Die FIB-Säule
  \begin{scope}[scale=2]
    \begin{scope}[yshift=0.2]
       Beschleunigung und fokussierung
    \begin{scope}[yshift=-1.4cm]
      { % Rückseite
        \path[fib background vert]
          (-0.7,0.2) arc (180:360:0.7 and 0.03) -- (0.7,-1.2) arc (360:180:0.7 and 0.03) --cycle;
      }
      { % Innenleben
        \path[fib lens thinn] % Linse
          (-0.3,-0.25) -- (-0.5,-0.25) -- (-0.5,-0.35) -- (-0.3,-0.35)
          (0.3,-0.25) -- (0.5,-0.25) -- (0.5,-0.35) -- (0.3,-0.35);
        \path[fib lens thick]
          (-0.45,-0.3) -- (-0.35,-0.3) (0.35,-0.3) -- (0.45,-0.3)
          (0,-0.3) coordinate (ionlens1)
          (-0.5,-0.25) coordinate (linse1);
        \path[fib quadrupole] % quadrupole 1
          (0,-0.45) ellipse (0.33cm and 0.01cm)
          (0,-0.65) ellipse (0.33cm and 0.01cm)
          (-0.35,-0.45) -- ++(0,-0.2) (-0.2,-0.45) -- ++(0,-0.2)
          (0.35,-0.45) -- ++(0,-0.2) (0.2,-0.45) -- ++(0,-0.2)
          (-0.35,-0.45) coordinate (quadA);
        \path[fib lens thick]
          (-0.25,-0.45) -- (0.25,-0.45)
          (-0.25,-0.65) -- (0.25,-0.65);
        \path[fib lens thick] % Blende
          (-0.7,-0.75) -- (-0.05,-0.75) (0.05,-0.75) -- (0.7,-0.75) coordinate[midway] (blende)
          (0,-0.75) coordinate (ionblende);
        \path[fib quadrupole] % quadrupole 2
          (0,-0.85) ellipse (0.33cm and 0.01cm)
          (0,-1.05) ellipse (0.33cm and 0.01cm)
          (-0.35,-0.85) -- ++(0,-0.2) (-0.2,-0.85) -- ++(0,-0.2)
          (0.35,-0.85) -- ++(0,-0.2) (0.2,-0.85) -- ++(0,-0.2)
          (-0.35,-0.85) coordinate (quadB);
        \path[fib lens thick]
          (-0.25,-0.85) -- (0.25,-0.85)
          (-0.25,-1.05) -- (0.25,-1.05);
      }
      \begin{scope} % Gehäuse
        \path[clip,decoration={random steps, segment length=6pt, amplitude=2pt}]
          (0.7,0.3) -- (0.7,-1.3)
          -- (0.6,-1.3) decorate{ ..controls (0.5,-0.6).. (0.6,0.3)} --cycle
          (-0.7,0.3) -- (-0.6,0.3) decorate{ ..controls (-0.5,-0.6).. (-0.6,-1.3)}
          -- (-0.7,-1.3) --cycle;
        \path[fib housing vert]
          (-0.7,0.2) arc (180:0:0.7 and 0.03) -- (0.7,-1.2) arc (0:180:0.7 and 0.03) --cycle;
      \end{scope}
      { % Ionenpumpe extern
        \path[fib housing]
          (0.7,-0.1) rectangle (0.9,-0.6);
        \path[fib housing]
          (0.9,-0.15) rectangle (0.95,-0.2) (0.95,-0.15) coordinate (ionenpume)
          (0.9,-0.55) rectangle (0.95,-0.5);
        \path[fib housing horz]
          (0.9,-0.25) rectangle (1.3,-0.45);
      }
    \end{scope}
    \begin{scope}[yshift=-2.8cm]
      % Optik und Ablenkteile
      { %Rückseite
        \path[fib background vert]
          (-0.8,0.2) arc (180:360:0.8 and 0.03) -- (0.8,-1.5) arc (360:180:0.8 and 0.03) --cycle;
        \path[fib background]
          (1.3,0.3) rectangle (2.4,-1.1);
      }
      { % Innenleben
        \path[fib blanker] % blanker
          (-0.3,0.1) rectangle (-0.25,-0.2)
          (0.3,0.1) rectangle (0.25,-0.2)
          (-0.3,0.1) coordinate (blanker);
        \path[fib lens thick]
          (-0.3,-0.05) -- (-0.4,-0.05) (0.3,-0.05) -- (0.4,-0.05);
        \path[fib lens thick] % Faradaykäfig
          (-0.3,-0.25) -- (-0.3,-0.35) -- (-0.15,-0.35) -- (-0.15,-0.25)
          (-0.3,-0.25) coordinate (faraday)
          (0.3,-0.25) -- (0.3,-0.35) -- (0.15,-0.35) -- (0.15,-0.25);
        \path[fib octopole] % octopole 1
          (0,-0.4) ellipse (0.38cm and 0.01cm)
          (0,-0.6) ellipse (0.38cm and 0.01cm)
          (-0.4,-0.4) -- (-0.4,-0.6) (0.4,-0.4) -- (0.4,-0.6)
          (-0.27,-0.4) -- ++(0,-0.2) (-0.1,-0.4) -- ++(0,-0.2)
          (0.27,-0.4) -- ++(0,-0.2) (0.1,-0.4) -- ++(0,-0.2)
          (0,-0.5) coordinate (ionocto1)
          (-0.4,-0.4) coordinate (octoA);
        \path[fib octopole] % octopole 2
          (0,-0.7) ellipse (0.38cm and 0.01cm)
          (0,-1.05) ellipse (0.38cm and 0.01cm)
          (-0.4,-0.7) -- (-0.4,-1.05) (0.4,-0.7) -- (0.4,-1.05)
          (-0.27,-0.7) -- ++(0,-0.35) (-0.1,-0.7) -- ++(0,-0.35)
          (0.27,-0.7) -- ++(0,-0.35) (0.1,-0.7) -- ++(0,-0.35)
          (0,-0.88) coordinate (ionocto2)
          (-0.4,-0.7) coordinate (octoB);
        \path[fib mirror]
          (0.4,-0.4) -- (0.6,-0.2) -- (0.4,-0.2) -- cycle;
        \path[fib mirror]
          (0.6,-1.2) -- (0.4,-1.4) -- (0.6,-1.4) -- cycle;
        \path[fib mirror]
          (-0.1,-1.4) -- (-0.025,-1.325) (0.025,-1.275) -- (0.1,-1.2) -- cycle;
        \path[fib mirror] % kamera innenleben
          (1.6,-0.2) -- (1.8,-0.4);
        \path[fib lens thinn]
          (1.6,-0.6) arc(100:80:0.575) arc(-80:-100:0.575) -- cycle;
        \path[draw=black!60, fill=black!20]
          (1.58,-0.82) -- (1.56,-0.97) -- (1.82,-0.97) -- (1.84,-0.82) --cycle;
        \path[draw=black!60, shading=ball, ball color=black!30]
          (1.7,-0.9) ellipse (0.1cm and 0.05cm);
        \begin{scope}
          \path[clip]
            (2.2,-0.3) circle (0.1cm);
          \path[draw=black!80, line width=0.04cm]
            (2.2,-0.3) circle (0.1cm)
            (2.1,-0.2) -- (2.3,-0.4)
            (2.1,-0.4) -- (2.3,-0.2);
        \end{scope}
        \path[fib lens thinn]
          (1.9,-0.2) arc(170:190:0.575) arc(-10:10:0.575) -- cycle;
      }
      \begin{scope} % externes Gehäuse
        \path[clip,decoration={random steps, segment length=6pt, amplitude=2pt}]
          (0.8,0) -- (1.3,0) -- (1.3,0.3) -- (2.4,0.3) -- (2.4,-1.1) -- (1.3,-1.1) -- (1.3,-0.6) -- (0.8,-0.6) -- (0.8,-0.1) -- (1.4,-0.1)
          decorate{ .. controls (1.4,-0.5) .. (1.6,-1) .. controls (2.3,-1) .. (2.3,-0.1) .. controls (1.8,0.2) .. (1.4,0)}
          -- (1.4,-0.1) -- (0.8,-0.1) --cycle;
        \path[fib housing horz]
          (0.8,0) rectangle (1.3,-0.6);
        \path[fib housing]
          (1.3,0.3) rectangle (2.4,-1.1);
      \end{scope}
      \begin{scope} % Gehäuse
        \path[clip,decoration={random steps, segment length=6pt, amplitude=2pt}]
          (0.8,0.3) -- (0.8,-1.6)
          -- (0.6,-1.6) decorate{ ..controls (0.8,-0.6).. (0.6,0.3)} --cycle
          (-0.8,0.3) -- (-0.6,0.3) decorate{ ..controls (-0.4,-0.6).. (-0.6,-1.6)}
          -- (-0.8,-1.6) --cycle;
        \path[fib housing vert]
          (-0.8,0.2) arc (180:0:0.8 and 0.03) -- (0.8,-1.5) arc (0:180:0.8 and 0.03) --cycle;
      \end{scope}
    \end{scope}
    \begin{scope}[yshift=-4.5cm]
      % Deckel
      { % Rückwand
        \path[fib background vert]
          (-0.8,0.2) arc (180:360:0.8 and 0.03) -- (0.8,-0.6) arc (360:180:0.8 and 0.03) -- cycle;
        \path[fib background vert]
          (0.8,-0.6) arc (360:180:0.8 and 0.03) -- (-0.3,-1) arc (180:360:0.3 and 0.01) -- cycle;
      }
      { % Innenleben
        \path[fib mirror]
          (-0.15,-0.4) arc (-75:-50:0.25) -- (-0.05,-0.4) -- cycle;
        \path[fib mirror]
          (0.15,-0.4) arc (-105:-130:0.25) -- (0.05,-0.4) -- cycle;
        \path[fib mirror]
          (-0.2,-0.1) arc (105:125:0.8) coordinate (tmp) -- (tmp |- -0.2,-0.1) --cycle;
        \path[fib mirror]
          (0.2,-0.1) arc (75:55:0.8) coordinate (tmp) -- (tmp |- 0.2,-0.1) --cycle;
        \path[fib lens thinn] % 2. Linse
          (-0.15,-0.65) -- (-0.3,-0.65) -- (-0.3,-0.75) -- (-0.15,-0.75)
          (0.15,-0.65) -- (0.3,-0.65) -- (0.3,-0.75) -- (0.15,-0.75);
        \path[fib lens thick]
          (-0.27,-0.7) -- (-0.17,-0.7) (0.17,-0.7) -- (0.27,-0.7)
          (0,-0.7) coordinate (ionlens2)
          (-0.27,-0.65) coordinate (linse2);
      }
      \begin{scope} % Gehäuse
        \path[clip,decoration={random steps, segment length=6pt, amplitude=2pt}]
          (-0.8,0.3) -- (-0.6,0.3) decorate{ ..controls (-0.5,-1.3) and (0.5,-1.3).. (0.6,0.3)}
          -- (0.8,0.3) -- (0.8,-1) -- (-0.8,-1) -- cycle;
        \path[fib housing vert]
          (-0.8,0.2) arc (180:0:0.8 and 0.03) -- (0.8,-0.6) arc (0:180:0.8 and 0.03) -- cycle;
        \path[fib housing vert]
          (0.8,-0.6) arc (0:180:0.8 and 0.03) -- (-0.3,-1) arc (180:0:0.3 and 0.01) -- cycle;
      \end{scope}
    \end{scope}
    \begin{scope}[yshift=-6cm, scale=0.5]
      % Probe
      \path[draw, rounded corners=1pt]
        (-1,-0.2) rectangle (1,-0.3);
      \path[draw, fill, top color=black!5, bottom color=black!20, rounded corners=2pt]
        (-0.5,0) -- (-0.5,-0.18) -- (0.5,-0.18) -- (0.5,0) -- (0.2,0) -- (0,-0.07) -- (-0.2,0) -- cycle
        (0,-0.07) coordinate (target);
      \path[draw, fill=black!60]
        (-0.5,-0.07) -- (-0.55,-0.07) to[out=180, in=0] (-0.6,-0.13) {[rounded corners=1pt] -- (-0.68,-0.13) --
          (-0.68,-0.2)} -- (-0.6,-0.2) to[out=0, in=180] (-0.55,-0.14) -- (-0.5,-0.14) -- cycle;
      \path[draw, fill=black!60]
        (0.5,-0.07) -- (0.55,-0.07) to[out=0, in=180] (0.6,-0.13) {[rounded corners=1pt] -- (0.68,-0.13) --
          (0.68,-0.2)} -- (0.6,-0.2) to[out=180, in=0] (0.55,-0.14) -- (0.5,-0.14) -- cycle;
    \end{scope}
    \begin{scope}[yshift=-5.7cm, rotate around={-30:(-0.75,0.2)}]
      % Szintillator
      \path[draw=black!80, line width=0.03cm] % 1. Antenne
        (-0.7,0.2) -- (-0.4,0.15) -- (-0.1,0.2);
      \path[fib housing horz]
        (-0.9,0.3) -- (-0.6,0.25) arc(90:270:0.1 and 0.15) -- (-0.9,0) arc(270:90:0.1 and 0.15) --cycle;
      \path[fib housing]
        (-0.6,0.1) ellipse (0.1 and 0.15);
      \begin{scope}
        \path[fib housing]
          (-0.6,0.1) ellipse (0.07 and 0.11);
        \path[clip]
          (-0.6,0.1) ellipse (0.07 and 0.11);
        \path[shading=ball, ball color=black!30]
          (-0.5,0) circle (0.4);
      \end{scope}
      \path[draw=black!80, line width=0.03cm] % 2. Antenne
        (-0.9,0.05) -- (-0.6,0) -- (-0.4,-0.2);
    \end{scope}
    \begin{scope}[yshift=-6cm]
      % Gasnadel
      \path[fib housing horz]
        (2,0.7) -- (0.35,0.3) -- (0.1,0.1) -- (0.1,0.05) -- (0.4,0.25) -- (2,0.6) -- cycle;
    \end{scope}
    \begin{scope} % Strahlen
      % Ionen
      \path[draw=black!80, dashed]
        (source) -- (emitter)
        (emitter) -- (ionlens1 -| -0.23,0) -- (ionblende -| 0.32,0)
        (ionblende -| 0.02,0) -- (ionocto1 -| 0.028,0) -- (ionocto2 -| 0.03,0) -- (ionlens2 -| 0.07,0) --
        (target) --
        (ionlens2 -| -0.07,0) -- (ionocto2 -| -0.03,0) -- (ionocto1 -| -0.028,0) -- (ionblende -| -0.02,0)
        (ionblende -| -0.32,0) -- (ionlens1 -| 0.23,0) -- (emitter);
      \path[fill=white, opacity=0.3]
        (emitter) -- (ionlens1 -| -0.23,0) -- (ionblende -| 0.32,0) --
        (ionblende -| 0.02,0) -- (ionocto1 -| 0.028,0) -- (ionocto2 -| 0.03,0) -- (ionlens2 -| 0.07,0) --
        (target) --
        (ionlens2 -| -0.07,0) -- (ionocto2 -| -0.03,0) -- (ionocto1 -| -0.028,0) --
        (ionblende -| -0.02,0) -- (ionblende -| -0.32,0) -- (ionlens1 -| 0.23,0) -- cycle;
      % Licht
      \path[draw=red]
        (1.6,-3) -- (0.6,-3) -- (0.6,-4) -- (0.1,-4) -- (0.1,-4.85) -- (0.34,-4.67) -- (target)
        (1.8,-3.2) -- (0.4,-3.2) -- (0.4,-4.2) -- (-0.1,-4.2) -- (-0.1,-4.85) -- (-0.34,-4.67) -- (target);
      \path[draw=red,->]
        (2.1,-3.1) -- (1.9,-3) -- (1.85,-3);
      \path[draw=red,->]
        (2.1,-3.1) -- (1.9,-3.2) -- (1.85,-3.2);
      \path[draw=red]
        (1.85,-3) -- (1.6,-3)
        (1.85,-3.2) -- (1.8,-3.2);
      \path[draw=red,->]
        (1.6,-3) -- (1.6,-3.3);
      \path[draw=red,->]
        (1.8,-3.2) -- (1.8,-3.3);
      \path[draw=red]
        (1.7,-3.7) -- (1.6,-3.4) -- (1.6,-3.3)
        (1.7,-3.7) -- (1.8,-3.4) -- (1.8,-3.3);
    \end{scope}
    % Beschriftung
    \begin{scope}[arrow]
      \path[draw] (0.9,0.3) node[anchor=west] {Galliumquelle mit Heizwendel} to[out=180, in=45] (0.2,-0.3);
      \path[draw] (1.5,-0.6) node[anchor=west] {\english{extractor}} to[out=180, in=45] (extractor);
      \path[draw,shorten >=0.1cm] (1.5,-0.3) node[anchor=west] {\english{suppressor}} to[out=180, in=45] (suppressor);
      \path[draw] (-0.7,0.5) node[anchor=east] (tmp) {Ionenpumpe Quelle} (tmp) to[out=-90, in=180] (-1.3, -0.2);
      \path[draw,shorten >=0.1cm] (-1.1,-1.2) node[anchor=east] {Austritt} to[out=0, in=225] (emitter);
      \path[draw] (1.5,-1.3) node[anchor=west] {Ionenpumpe} to[out=180, in=45] (1,-1.5);
      \path[draw,shorten >=0.1cm] (-0.9,-1.8) node[anchor=east] (quad) {Quadrupole 1, 2} to[out=0, in=160] (quadA);
      \path[draw,shorten >=0.1cm]  (quad) to[out=0, in=160] (quadB);
      \path[draw,shorten >=0.05cm] (-1.1,-1.4) node[anchor=east] {1. Linse} to[out=0, in=135] (linse1);
      \path[draw,shorten >=0.05cm] (1.5,-1.8) node[anchor=west] {Blende} to[out=180, in=60] (blende);
      \path[draw, shorten >=0.1cm] (-1.1,-2.3) node[anchor=east] {\english{blanker}} to[out=0, in=140] (blanker);
      \path[draw, shorten >=0.1cm] (-1.1,-2.7) node[anchor=east] {Faradaykäfig} to[out=0, in=140] (faraday);
      \path[draw, shorten >=0.1cm] (-1.1,-3.1) node[anchor=east] (okto) {Oktopole 1, 2} to[out=0, in=140] (octoA);
      \path[draw, shorten >=0.1cm] (okto) to[out=0, in=140] (octoB);
      \path[draw] (1.5,-2.1) node[anchor=west] {optische Einkopplung} to[out=180, in=70] (0.5, -2.9);
      \path[draw,shorten >=0.2cm] (2,-2.35) node[anchor=east] {Lichtquelle} to[out=0, in=50] (2.2,-3.1);
      \path[draw, shorten >=0.2cm] (2,-4.1) node[anchor=west] {CCD Kamera} to[out=180, in=-70] (1.7,-3.7);
      \path[draw] (1.5,-4.5) node[anchor=west] {Objektiv} to[out=180, in=20] (0.5,-4.7);
      \path[draw] (-1.1,-4.7) node[anchor=east] {2. Linse} to[out=0, in=150] (linse2);
      \path[draw] (1.5,-5.1) node[anchor=west] {Gasinjektionsnadel} to[out=180, in=70] (0.7,-5.6);
      \path[draw] (1.5,-5.8) node[anchor=west] {Probe} to[out=180, in=20] (0.3,-6);
      \path[draw] (-1.1,-5.1) node[anchor=east] {Szintillator} to[out=0, in=110] (-0.8,-5.4);
      \path[draw] (-1.1,-6) node[anchor=east] {Antennen} to[out=0, in=-120] (-0.7,-5.9);
    \end{scope}
  \end{scope}
\end{tikzpicture}
\end{document}

S = ⎩ ⎨ ⎧ S_{l e f t} if x_{i}^{*} = x_{i - 1} S_{r i g h t} if x_{i}^{*} = x_{i} S_{mi d} if x_{i}^{*} = \frac{x _{i} + x _{i - 1}}{2}