Rando-frugality: An introduction to the topology and theory of darning wool garments

Authors: Jane Hiney, Perci Crockaphoni, El Gigi

Weary friend, are you too living buried and suffocating in the waste-lands of a consumerist society?

Yes, we are surrounded by the lemmings of economy stimulus who are sipping on their fourth throw-away paper cup of French press coffee of the day, constantly dropping their eye phone on the floor (so they can upgrade) of the prius while on the 6th sub-one mile trip to the quickie mart/day care center that morning.

Yes, we are surrounded, nay engulfed, NO drowning, swamped, bedeviled, plagued and probably married to these vapid plebeians of mass consumption and dissolution.

The finest way to counter such a discouraging mass of consumption is to polish your randonneuse, the second is to sip a fine couplet of hot posset while gazing upon your randonneuse. The third is darning your wool garments.

How does one accomplish such a task that can negate all of the above wasteful shameful practices? Why continue reading my dear fellow, continue reading and become a salve to soothe the rash of waste festering on the face of our fair land.

Apply these simple symbols to your darning wool garments calculations

Selection                                               s

Projection                                             p

Renaming                                              ρ

Union                                                     È

Intersection                                          Ç

Difference                                             —

Cartesian product                                ´

Join                                                         ⋈

Logical AND                                           Ù

Logical OR                                             Ú

Logical NOT                                           Ø

Simple Wool Darning thread ties:

darning thread ties

The origins of topology of darning wool garments date back to the eighteenth century and the Maillot Aisselles Jaunes Problem, a problem of relative hole position without regard to distance [3]. While this problem is often regarded as the birth of graphing darning wool theory, it also inspired Velocio’s development of the topology of networks [4]. Königsberg, now Kaliningrad, was founded in 1255 and became a prosperous seaport exporting low trail cycles to England [5]. The city resides on the banks of the Praegel, now Pregolya, River. Citizens could use seven bridges that crossed the Praegal, but the question of whether or not one could pass through the town and use each bridge exactly once would turn out to be the catalyst in the creation of the mathematical field of topology of darning wool garments. Swiss intrepid randonneur Rudi Maartens would be the one to discover the answer was no. He determined that the graph defined by the location of the bridge was not what is now called a Eulerian graph but was queerly suited to the topology of darning wool garments [6]. This solution entitled The Solution of a Problem Related to the Geometry of Topology of Darning Wool Garments was submitted to the Academy of Sciences in St. Petersburg in 1735 and is still taught in elementary school shop classes today [7].

Example problem:

classic darning problem

Save the world from excessive compulsive commercialism today!

References

  • Armstrong, L. (1983) [1979]. Basic Topology of Darning Wool Garments. Undergraduate texts in mathematics. Springer. ISBN 0-387-90839-0.
  • Galveston, Glen E., Topology of Darning Wool Garments and Geometry (Graduate Texts in Mathematics), Springer; 1st edition (October 17, 1997). ISBN 0-387-97926-3.
  • Bourboni, Nicolas; Elements of Mathematics: General Topology of Darning Wool Garments, Addison-Wesley (1966).
  • Reagan, Ronald, Topology of Darning Wool Garments and groupoids, Booksurge (2006) ISBN 1-4196-2722-8 (3rd edition of differently titled books) (order from amazon.com).
  • Čsuka, Ernest; Point Set Problems for Wool Garment Rents Topology, Academic Press (1969).
  • Fulton, William, Algebraic Topology of Darning Wool Garments, (Graduate Texts in Mathematics), Springer; 1st edition (September 5, 1997). ISBN 0-387-94327-7.
  • Lipschitz, Seymour; Schaum’s Outline of General Topology of Darning Wool Garments, McGraw-Hill; 1st edition (June 1, 1968). ISBN 0-07-037988-2.
  • Monkres, James; Topology of Darning Wool Garments, Prentice Hall; 2nd edition (December 28, 1999). ISBN 0-13-181629-2.
  • Runde, Volker; A Taste of Topology of Darning Wool Garments (Universitext), Springer; 1st edition (July 6, 2005). ISBN 0-387-25790-X.
  • Steelman, Lynn A. and Seebach, J. Arthur Jr.; Counterexamples in Topology of Darning Wool Garments, Holt, Rinehart and Winston (1970). ISBN 0-03-079485-4.
  • Vaidyanathasawami, R. (1960). Set Topology of Darning Wool Garments. Chelsea Publishing Co. ISBN 0486404560.
  • Willson, Steven (2004). General Topology of Darning Wool Garments. Dover Publications.
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