## You are here

HomePlanetMath graphics sandbox

## Primary tabs

# PlanetMath graphics sandbox

$\xymatrix{1&2\ar@{-}[d]&3\ar@{-}[r]\ar@{-}[d]\ar@{-}[dr]&4&5\ar@{-}[r]&6\ar@{-% }[d]\\ &7&8&9&10\ar@{-}[r]&12}$ |

Some text, yada, yada, yada. $10\spadesuit~{}A\clubsuit~{}J\heartsuit$

Silver rectangle with a horizontal line plopped down somewhere.

A Collatz tree of height 12.

$\xymatrix{96\ar[d]&17\ar[dr]&104\ar[d]&106\ar[d]&640\ar[d]&672\ar[d]&113\ar[dr% ]&680\ar[d]&682\ar[d]&4096\ar[d]\\ 48\ar[d]&&52\ar[d]&53\ar[dr]&320\ar[d]&336\ar[d]&&340\ar[d]&341\ar[dr]&2048\ar% [d]\\ 24\ar[d]&&26\ar[d]&&160\ar[d]&168\ar[d]&&170\ar[d]&&1024\ar[d]\\ 12\ar[d]&&13\ar[drr]&&80\ar[d]&84\ar[d]&&85\ar[drr]&&512\ar[d]\\ 6\ar[d]&&&&40\ar[d]&42\ar[d]&&&&256\ar[d]\\ 3\ar[drrrr]&&&&20\ar[d]&21\ar[drrrr]&&&&128\ar[d]\\ &&&&10\ar[d]&&&&&64\ar[d]\\ &&&&5\ar[drrrrr]&&&&&32\ar[d]\\ &&&&&&&&&16\ar[d]\\ &&&&&&&&&8\ar[d]\\ &&&&&&&&&4\ar[d]\\ &&&&&&&&&2\ar[d]\\ &&&&&&&&&1}$ |

Suppose $K$ and $J$ are both the trefoil knot.

Type of Math Object:

Data Structure

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

51-00*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Comments

## picture request

Since this entry seems to be a hub of graphics activity, I'm

posting my request here.

I am working on an entry on basic methods of enumerative

combinatorics. Right now I'm working on the principle of

inclusion-exclusion. In its most basic form, this says that

\[

|S| + |T| = |S\cup T| + |S\cap T|.

\]

Intuitively this is true because if you mark each element of

$S$ with a daub of blue paint and then mark each element of

$T$ with a daub of red paint, then each element of $S\cup T$

will have at least one daub of paint on it, red or blue, and

each element of the intersection $S\cap T$ will have two daubs

of paint on it.

What I would like to include to illustrate this is a Venn diagram

showing the intersection of two circles, one marked $S$ and

one marked $T$. The components $S\setminus T$ and $T\setminus S$

each should have an x inside, while the intersection should have

two xs.

Is anyone willing or able to contribute such a picture?