Recently Published 2000-2004

Infinte Sceptre Sequence

©1997-2003, Alvy Ray Smith, All Rights Reserved.

 

Captain Bethuel Riggs of the Revolutionary War Died in Missouri, Not Ohio

Paper, published, The American Genealogist (TAG), Jan/Apr 2004, vol. 79, nos. 1-2, 34-37.

ABSTRACT. Bethuel Riggs, a Primitive Baptist elder and Revolutionary War captain, traveled throughout his life, for god or for country, living in many states and starting at least five churches. His birth in Mendham Township, Morris County, New Jersey in 1757 is not in question, but his date of death is often erroneously stated, and two states claim to be his place of death. As will be demonstrated, official records are the source of the ambiguity. The purpose of this article is to set these records straight: Elder and Captain Bethuel Riggs died on 25 July 1835 in Lincoln County, Missouri.

 

Dr. John Durand (1664-1727) of Derby, Connecticut: His Family Through Four Generations, Featuring the Branch of His Youngest Son, Ebenezer Durand, Through Ten Generations to 2003

Book, 586 pages, 100 illustrations, 1,955 footnotes, full name and place indexes, published 24 September 2003, Newbury Street Press, Boston

See webpages for book

 

Indiana Descendants of Dr. John Durand, 1664-1727: Excerpts from Dr. John Durand of Derby, Connecticut, and His Family, Part 1: Samuel and Son Orson

Paper, part 1 published, The Hoosier Genealogist, 5 pages, Spring 2003, 43[2003]: 59-62 (plus cover); part 2 published, 4 pages, Summer 2003, 43[2003]:127-30.

ABSTRACT. This paper concentrates on the descendants of Dr. John Durand (see book Dr. John Durand of Derby, Connecticut, and His Family) who found their way to Indiana and influenced Indiana genealogy.

 

How I Was Inspired to Publish a Family History: the Durands of Colonial Connecticut

Paper, published, New England Ancestor, 3 pages, Holiday 2003, 4[2003]28-30.

ABSTRACT. This paper summarizes the various motivations that inspired me to write the Durand book (see book Dr. John Durand of Derby, Connecticut, and His Family).

 

An Old LITTELL Family Bible

Paper, published, NGS (National Genealogical Society) Quarterly, vol. 90, no. 4, December 2002 [plus front cover and inside front cover], 273-81

ABSTRACT. I bought an old family Bible from an email correspondent who claimed it contained many of my family surnames. It turned out to be an old Littell family Bible, printed in 1793. This paper is a transcription of it into easily readable form. A careful analysis shows it to validate and expand somewhat the data for a single family in the well-known Family Records or Genealogies of the First Settlers of Passaic Valley, by John Littell, 1852. See Littell Bible for a memo which is the predecessor to this paper, including actual images of the Bible pages with genealogical information. I have donated the Bible itself and digital images of its genealogical pages to the NEHGS (New England Historic Genealogical Society) in Boston. See erratum below, correcting an error discovered after publishing.

ERRATUM: page 277, line 6 (hence page 281, last line): Replace the second, or death, year "1806" with "180[7?]". Cf., fifth item below under Westfield gravestones, which establishes the year to be 1807.

ADDITION: page 280, person 15, Mary Clark Littell: She was interred, on 30 March 1881, in Westfield, Union Co., New Jersey. [Source: Deaths in the New York Post, NEHGS database online at <www.NewEnglandAncestors.org>, article dated 30 Mar. 1881: "Wed 30th Mary Clark wid Gilbert C Briggs and dau late Caleb M Littell of City Interment Westfield NJ."]

ADDITIONS: The source for the following five items is Herbert A. Halsey, Guide to the Colonial Cemetery of the Presbyterian Church in Westfield, New Jersey, online at David Kane, Westfield Presbyterian Cemetery Tombstone Inscriptions, <www.WestfieldNJHistory.com/files/llrecord.htm> (downloaded 16 June 2003):

(1) page 280, person 1, Sarah Marsh: She died 22 February 1802, aged 32 years, and is buried in the Westfield Presbyterian Cemetery as "Acken, Sarah, wife of Jonathan," Westfield, Union Co., New Jersey. The computed birthdate for her is 22 February 1770.

(2) pages 280-81, person 1, Ann[a] (Maxwell) Littell: She died 11 April 1841, aged 72 yrs. 1 mo. 4 dy., and is buried in the Westfield Presbyterian Cemetery as "Sayre, Anne, wife of William (who d. 1828); eldest daughter of Caleb and Susannah Maxwell [widow of Anthony Littell and of Wm. Sayre]," and as "Acken, Anne, widow of Jonathan who d. 1807; d. of Caleb and Susannah Maxwell," Westfield, Union Co., New Jersey. The computed birthdate for her is 7 March 1769.

(3) age 281, person 4, HANNAH SQUIER: She died 4 July 1868, aged 76 yrs., and is buried in the Westfield Presbyterian Cemetery as "wife of Wm. Acken," Westfield, Union Co., New Jersey. The computed birthdate for her is 4 July 1792.

(4) page 281, person 5, Jonathan Acken: He died 11 March 1796, aged 4 yr. 6 mo., and is buried in the Westfield Presbyterian Cemetery as "son of Jonathan and Sarah Acken," Westfield, Union Co., New Jersey. The computed birthdate for him is 11 September 1791.

(5) page 281, person 11, Joseph Acken: He died 19 February 1807, aged 5 mo. 5 dy., and is buried in the Westfield Presbyterian Cemetery as "son of Jonathan and Anna Acken," Westfield, Union Co., New Jersey. The computed birthdate for him is 14 September 1806.

 

The Reality of Simulated Actors

Communications of the ACM, Vol 45, No 7, Jul 2002, 36-9

ABSTRACT: I revisit the topic of the Nov 2000 Scientific American article, with tighter predictions and perceptions. The subhead chosen by the editor is: The acting of actors will survive the digital revolution; their on-screen appearance may not.

 

Digital Paint Systems: An Anecdotal and Historical Overview

IEEE Annals of the History of Computing, Vol 23, No 2, Apr-Jun 2001, 4-30 [and cover]

ABSTRACT: This document is based on lectures by the author and Dick Shoup [his article is pp 32-37 of the same issue] on early paint programs at the Computer History Museum in California, January 2000. A chronology of pre-1980 digital paint systems is presented, followed by a detailed anecdotal history of some of them, emphasizing the author's experience at Xerox Palo Alto Research Center (PARC) and the New York Institute of Technology (NYIT). See sampling of early paint images, presented in this article.

 

Infinite Regular Hexagon Sequences on a Triangle

Experimental Mathematics, Vol 9, No 3, Nov 2000, 397-406

ABSTRACT: The well-known dual pair of Napoleon equilateral triangles intrinsic to each triangle is extended to infinite sequences of them, shown to be special cases of infinite regular hexagon sequences on each triangle. A set of hexagon-to-hexagon transformations, the hex operators, is defined for this purpose, a set forming an abelian monoid under function composition. The sequences result from arbitrary strings of hex operators applied to a particular truncation of a given triangle to a hexagon. The deep structure of the sequence constructions reveals surprising infinite sequences of non-concentric, symmetric equilateral triangle pairs parallel to one of the sequences of hexagons and provides the most visually striking contribution. Extensive experimentation with a plane geometry educational program inspired all theorems, proofs of which utilize eigenvector analysis of polygons in the complex plane.

The figure above, from the paper, shows the first two elements of two infinite "sceptre" sequences and two infinite regular hexagon sequences, for any triangle.  A sceptre is a pair of congruent equilateral triangles with parallel sides, such that a vertex of each lies on a side of the other - see the figure, where a red-blue pair of equilaterals forms a sceptre. Its name is derived from "symmetric, congruent, equilateral pairs of triangles". The hexagon sequences are centered over the centroid of the given triangle, which is almost obscured by the other forms.  (It is almost entirely enclosed by the gray parallelogram.)  Notice that the sceptres have sides parallel one of the sequences of hexagons, and their diagonals (dashed line) pass through the centroid of the given triangle. Less obvious: If you join the topmost red triangle vertex to the leftmost blue triangle vertex, the line formed is parallel the other sequence of regular hexagons.

Sketches and scripts for The Geometer's Sketchpad (TGS), illustrating the theorems, are available. The file hex.txt is a text file explaining the other files available. New! A Java version of one of the theorems is now online. Try out the theorem interactively!

See other recent geometric art.

 

Digital Humans Wait in the Wings

Scientific American, Nov 2000, 72-78

SUBTITLE (the "deck"): Characters, scenes and entire movies have been crafted digitally. But can animators create realistic digital humans to star in computer-generated films? Actors want to know

ABSTRACT: The completely computer-generated movie is already with us, but is still in the realm of cartoons. When will a "live-action" movie be computer generated? In particular, will human actors be replaced by computer graphic simulations? It is argued that the representations of actors might be replaced but not the acting. In other words, it is valuable to separate the actor from his or her representation, as we do in animation already and as we do on the internet too, when using avatars. The article also estimates, with as much accuracy as can be mustered, when we might expect the representations of humans might reach the point of realism: Not so soon as sometimes predicted.

 

Man's Most Malleable, a poem

Tools of Vision, by Neelon Crawford, Oct 2000, 35

Friend and expert photographer, Neelon Crawford, is publishing a book of his photographs of "big science" - those superb instruments such as telescopes and accelerators that are used to see the largest and smallest things in our universe. He has asked scientists at the various facilities and his friends to contribute words on the general topic of "tools of vision". My contribution is this poem, my first in print. Tools of Vision is the exhibition catalog for Neelon's photographs on exhibit in the Rotunda Gallery of the National Academy of Sciences, Washington DC, 26 Sep 2000 - 15 Jan 2001. See Polar Fine Arts for photos and writings.