**Sundry Obscure Topics**

Dave Barber

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Algebra:

- ◊◊ Ternary quasigroups over small sets Jun 2010
- ◊ 3-factor 8-dimension cross product Apr 2014
- ◊ 480 varieties of octonion multiplication Nov 2015
- ◊ Generalized Lichtenberg ratios Dec 2019; complex values added Jan 2022
- Modular fibonacciësque sequences Oct 2016
- A broad generalization of matrix multiplication Jan 2014
- Dozen-score operations Jan 2013
- Some counterparts to the golden ratio Mar 2014
- Some algebra with ternary multiplication #1 Mar 2010
- Some algebra with ternary multiplication #2 Jul 2012
- Yet another generalization of boolean algebra Jan 2009
- Multicomplex numbers Dec 2015
- Cosines and sines of multiples of π/34 Feb 2016
- Some identities for a family of cross products Jul 2016
- Powers of Eisenstein integers Feb 2022
- Integer emphasis:
- ◊ Radicalized integer quaternions Nov 2014; octonions added Apr 2016
- ◊ Quintright integral domain Aug 2018
- Septright integral domain Aug 2018
- Cosine integral domains Mar 2016
- Algebras over ordered triples of integers Jul 2019

- Integer division Mar 2016
- Prime factorizations of Lipschitz quaternions Nov 2011
- Integral octonions Apr 2016
- Modular Latin squares Apr 2020

Geometry:

- Plinthology:
- ◊◊ Hexagonal toy bricks Nov 2012
- Code for three-dimensional printers Mar 2020

- Rectangular toy bricks Sep 2012
- Equal-area dogleg bricks Jun 2015
- BS 4729 angle bricks Jun 2015
- Flemish bond with long bricks Mar 2009

- ◊◊ Hexagonal toy bricks Nov 2012
- ◊ Toy train track Nov 2012
- 36-degree system revisited Nov 2017

- ◊ Compass points Jun 2008
- ◊ Deltoidal Hexecontahedra Dec 2009
- Multiple threads on threaded fasteners Apr 2020
- Rings of regular polygons Jul 2020
- A multidimensional generalization of the regular hexagon Mar 2013
- Simplex coördinates Jul 2012
- Quincunx Jul 2006
- Convex deciphis Dec 2012
- Grids of circles Sep 2019
- Substitution of Bézier curves in polygrams Nov 2019
- Tilings:
- Interlocking floor tiles Jul 2017
- Tessellations of equiangular hexagons Dec 2011
- Oblique Truchet tiles Jan 2017
- Trapezoid tables Aug 2012
- Triangular modules for miniature golf Jun 2019
- Epsilon tessellations Aug 2022

Other math:

- ◊ A parameterization of trigometric functions Dec 2015
- Some higher-order trigonometric functions Jan 2016
- Quaternion differentiation Nov 2014
- Collections of distant subsets Feb 2019
- Boolean operations for partitions of integers Mar 2019

Computer topics:

- C++ family:
- Annulus container for C++ Dec 2014
- Implementing arrays in C++:
- in two dimensions Jan 2014
- in three dimensions Jan 2014
- in any number of dimensions Jan 2014

- Array aliases in C Jan 2014
- Calculating multinomial coefficients in C++ Dec 2013
- Four C++ classes for managing permutations Dec 2016

- JavaScript:
- ◊ Two-dimensional radio buttons Nov 2015
- Double-selection radio buttons Nov 2015

- Unicode alphanumeric characters for math Jan 2022
- Quantum entanglement measure Aug 2011
- Oblique slices of a color cube Jul 2008
- Unicode box-drawing characters Jul 2008
- RGB-HSB color conversion in PostScript Feb 2017
- CPU architecture with 17-bit word size Jul 2011

Calculators (in JavaScript):

- ◊ Axonometric calculator Jun 2012
- Tetrahedron calculator Oct 2013
- Quaternion calculator Dec 2011
- Complex-number calculator Oct 2015

Paper:

- International paper sizes May 2012
- Paper basis Table Jul 2006
- Carbonless copy sets Oct 2010

Games:

- Playing cards:
- ◊ Set card game Nov 2007
- ◊ Star-pip playing cards Mar 2015
- ◊ East Point Pinochle Apr 2015
- Contraconquer Jan 2019
- Shuffling large packs of cards Feb 2019
- Leap sequences for melds Feb 2019
- Variants for the Game of Trains Mar 2019
- Never Over May 2012
- WarGops Apr 2012
- Xovimat playing cards Nov 2007
- Vertical combinations for Poker hands Feb 2015
- Somerset Klondike May 2015
- Linear Modular Sequence Mar 2018

- Board games:
- ◊ Modular linear sequence Sep 2016
- Bendominoes:
- Placement diagram for curved tiles Jan 2017
- Polygonal tile shape Jan 2017

- Sesquidominoes Dec 2010
- Bingo on hexagonal grid Nov 2018
- Corporate Gigabucks Jun 2014
- Catan board May 2014

- Others:
- ◊ Bowling-and-a-half Jan 2017
- Tantrix Rock:
- Permucolor dice Mar 2006
- Springfield parimutuel Sep 2014
- Baseball scoring variant Sep 2019

Public affairs:

- Two-dollar bills:
- States on the Lincoln Memorial Aug 2008
- Yankee Routes Sep 2007
- Analogues of blue Hawaiian STOP signs Jun 2022

Miscellaneous:

- ◊ Guitar Speakers Aug 2010
- Names of musical pitch intervals Mar 2014
- Numbering system for crayon colors Mar 2014
- Etymology of
*unicorn*Jan 2011 - Traditional volume measures Nov 2001
- Useful terminology for woo-woo Aug 2019

◊ *indicates* Dave's Faves

It is intentional that these pages use the simplest web technology possible, so as to maximize compatibility with various browsers, and to minimize internet bandwidth consumption. The author does not attempt to stay *au courant* with the HTML standards *du jour*; in part because HTML, although it is an excellent tool, has led a confused existence, with some markups indicating how text should look, and other markups indicating how the text should be interpreted.

I am a firm adherent of Sturgeon's Law, which says that ninety percent of everything is garbage. I have no doubt that Sturgeon's Law applies to this very website. Had I any way to discern which of the above pages were indeed vapid trash, I would be pleased to promptly delete them; I welcome nominations.

A persistent recursivist might inquire:

- Is ninety percent of Sturgeon's Law garbage?
- Does ninety percent of ostensible garbage fall so short of the standard of what garbage ought to be that it should be reclassified as garbage wannabe?

Atlanta driving rules:

- If somebody is tailgating you, you're not driving fast enough.
- If you're not tailgating somebody, you're not driving fast enough.
- If it's raining, you're going to be in a traffic jam somewhere on your trip. Therefore, on those parts of your route where traffic is not jammed, you need to drive faster than normal to make up the time you lose in the traffic jam. In fact, the heavier the rain, the faster you should drive, particularly at night. Also, be sure to run red lights.

Among the glories of mensuration in the United States is the following:

- An ounce of feathers weighs
*less*than an ounce of gold. - A pound of feathers weighs
*more*than a pound of gold.

Feathers, and most other things, are weighed by the avoirdupois ounce, which is about 28.35 grams. However, gold and other precious metals are weighed by the troy ounce, which is about 31.10 grams. So the ounce of feathers weighs *less* than the ounce of gold.

Meanwhile, an avoirdupois pound is sixteen avoirdupois ounces, making the pound of feathers weigh about 453.59 grams. But a troy pound is only twelve troy ounces, which works out to about 373.24 grams. So the pound of feathers weighs *more* than the pound of gold.

With all the attention given to the Ides of March, often overlooked is that every month has an Ides, observed on the following days:

Jan 13 | Apr 13 | Jul 15 | Oct 15 |

Feb 13 | May 15 | Aug 13 | Nov 13 |

Mar 15 | Jun 13 | Sep 13 | Dec 13 |

The English word *Ides* comes from the fourth-declension Latin noun *Idus*, so a suitable English adjective would be *Idual*, on the model of Latin *spiritus* whence English *spiritual*.

Assorted musings:

• Long live the obelus **÷** as a symbol for division! The explicit multiplication symbol **×**, although sadly neglected, is also deserving of use.

• We must teach our children Boolean algebra, because it is too simple for adults to learn.

• Beans, eaten directly from the can: real food for real men.

• *I calls 'em as I sees 'em.* — proverb often attributed to baseball umpires.

• LINGVA LATINA OPTIMISSIMA: Latin is the bestest.

• *I shall go to Korea.* — Dwight David Eisenhower

• Unshackle yourself from the mathematical ball-and-chain dating back to horse-and-buggy times: seek algebras wherein multiplication is not burdened by commutativity.

• Perfection is easy to attain if you set your standards low enough.

• I have suspended my support of Major League Baseball until the 1994 World Series takes place.

• In Neapolitan ice cream, the vanilla should be situated *between* the chocolate and strawberry; in other words the chocolate and strawberry should never adjoin. By the same token, in a Neapolitan citrus sherbet, the lemon should be located *between* the lime and orange. (The same principle applies to a three-layer cake.)

• What this world needs is a pinto bean that does not lose its spots when cooked.

• Bezier curves are remarkable for their simplicity, elegance, usefulness, computational efficiency, and generalizability.

• Don't trust any musical composer who doesn't know how and when to use double sharps and double flats.

• The best comic ever: They'll Do It Every Time.

Deeply-held binary convictions | |
---|---|

bad |
good |

Printed plaids | Woven plaids |

Books with glued-in pages | Books with sewn-in pages |

Bridge-size playing cards | Poker-size playing cards |

Five-line monthly calendars ("23/30", "24/31") | Six-line monthly calendars |

American paper sizes, e.g. letter = 8½ × 11 inches | International paper sizes, e.g. A4 = 297 × 210 millimeters |

Prescriptive grammar and vocabulary | Descriptive grammar and vocabulary |

Diet Coca-Cola | Coca-Cola Zero |

PC | Mac |

Sestertian monetary denominations, e.g. 1-
-5-10-2.5-50-100-25-500250 | Non-sestertian monetary denominations, e.g. 1-
-5-10-2-50-100-20-500200 |

Cubed ice | Crushed ice |

Infix calculator syntax | Postfix calculator syntax* |

* It can be argued that prefix syntax ought, by the principle of symmetry, to be held in the same high regard.

"You were under the impression

That when you were walking forwards

You'd end up further onward,

But things ain't quite that simple"

— "I've Had Enough", Quadrophenia, The Who.

*Version of Friday 5 August 2022*