Clark Kimberling

Welcome to my home page. Here you'll find various mathematical, historical, and musical topics, in many cases matched with biographical sketches. The mathematical topics include triangle geometry and number theory. The section on triangle geometry contains the world's largest internet collection of triangle centers. The number-theoretic topics deal mostly with integer sequences and arrays. The historical collection started out with 19th century scientists associated with the famous town, New Harmony, Indiana, located about 30 miles from Evansville. The collection has grown to include educators, writers, and artists. The music section consists of projects, including links to free downloadable scores and recordings. Ongoing projects include arranging and composing for groups of recorders. Below, you can click and listen to 75 duets and 117 trios performed by Japanese recorder artist Papalin.

Collection 1: African-American and Jamaican Melodies
Collection 2: Christmas Carols (available from Mel Bay Publications.)
Collection 3: Irish Melodies
Collection 4: Americana to 1865
Collection 5: Americana after 1865
Collection 6: British Melodies
Collection 7: Melodies by Women Composers
Collection 8: Eastern European and Jewish Melodies
Collection 9: American Indian Melodies
Collection 10: Latin American Melodies
Collection 11: African Melodies
Collection 12: Western European Melodies

Project 2. Compositions for church choirs, available from G.I.A. Publications:

Four Anthems for Mixed Voices and Handbells
Scripture and Season in Song
The Hills Are Hushed This Night of Nights
O God, Beneath Your Hand
O God, Who at the Dawn of Time
Ring Out the Glad Tidings
The King of Love My Shepherd Is
This Easter Morn
Awake with Timbrel and with Dance

Project 3. New hymn tunes, with texts by James Hart Brumm, John Core, Ralph Freeman, Daniel P. Merrick, and John Thornburg. The book is available from Wayne Leupold Editions; click Information.

Project 4. Henry Hart, a composer who lived in Evansville, Indiana (where I live) in the 1870's. Hart published minstrel tunes and music for social dance. The research led to the first of my biographical articles for Wikipedia: Henry Hart. The External Links section at the end will take you to three supplements:

Supplement I. Henry Hart and His Family Orchestra (Including Eli Lilly's Recollections)
Supplement II. Hazel Hart Hendricks and Her School
Supplement III. Myrtle Hart, Harpist

Project 5. Articles in The Hymn, the journal of The Hymn Society in the United States and Canada:

       Tunes Lost and Found: BIRSTAL, FOUNDRY, HOTHAM, TRUE ELIJAH, The Hymn 52, no. 1 (Jan., 2001) 21-30.

       Tunes Lost and Found: HELMSLEY, LEEDS, YORKSHIRE, WEDNESBURY, The Hymn 52, no. 2 (Apr., 2001) 25-36.

       Tunes Lost and Found: TRUMPET, LOVE-FEAST, ATHLONE, DERBY, The Hymn, no. 2 (Apr., 2002) 7-18.

       The Hymn Tunes of Richard Wayne Dirksen, The Hymn 53, no. 4 (Oct., 2002) 19-28.

       Hymn Tune Descants, Part 1: 1915-1934, The Hymn 54, no. 3 (July, 2003) 20-27.
          Reprinted in Journal of the Ralph Vaughan Williams Society 29 (Feb., 2004) 17-20.

       Hymn Tune Descants, Part 2: 1935-2001, The Hymn 55, no. 1 (Jan., 2004) 17-22.

       Three Native American Hymns, The Hymn 56, no. 2 (Spring 2005) 18-29.
          Regarding these hymns, see the Wikipedia article Joseph Renville.

Project 6. Christmas carols for flute with keyboard accompaniment: Tidings of Comfort and Joy.

Project 7. Duets for Flutes or Recorders for flutes, recorders (bass, tenor, alto, soprano, sopranino), or other instruments: DUETS - Publisher's description.

The duets are performed on various pairs of recorders, from contrabass up to sopranino, by Papalin:
Part 1: Duets 1-27
Part 2: Duets 28-50
Part 3: Duets 51-75

Project 8. Trios for Recorders or Flutes. For downloadble free scores, click Online Sheet Music: Recorder Trios.

The 117 trios in this collection are performed on various recorders, from contrabass up to sopranino, by Papalin:
Part 1: Trios 1-27
Part 2: Trios 28-58
Part 3: Trios 59-90
Part 4: Trios 91-117

For access to the vast collection of Papalin's recordings, IL DIVO "Papalin"

Neil Sloane's Online Encyclopedia of Integer Sequences (OEIS) is a treasury of mathematical patterns, including references, links, and comments. Many contributors have developed prototypical sequences that introduce newly discovered relationships among numbers, some proved and others conjectural. Here are several:

Accumulation arrays and chains, weight arrays: A144112, A185906, A185778
Adjective-noun sequences and conjectures: A055168- A055185 and A055186- A055191
Adjusted joint rank sequences: A186219, A186221, A186350
Augmentation arrays: A193091
Averaging arrays: A197737
Beatty arrays: A181661, A181886, A183988
Beatty discrepancy, complementary equations: A138253, A138330, A136496
Change-of-base functions (geometric fractals): A214969
Constants associated with special shapes: A188593, A188618, A188635, A195284 (Philo distance, incenter) A195304 (Philo distance, centroid)
Constants associated with extreme values: A196500
Constants associated with tangencies: A196625, A197016
Constants that solve transcendental equations: A196396, A196401, A196407, A197737, A197739
Continued fractions (including conjectures): A143515, A143527, A013659 (initialized continued fractions), A096654- A096658 (self-generating continued fractions)
Convolution arrays: A213500
Dispersions: A191426, A114537 (the primes)
Divided difference sequences: A204892
Double interspersion: A161179
Iteration from natural numbers to lower Wythoff sequence: A181108
Fission arrays (of polynomial sequences, infinite matrices) A193842, A202503 (Fibonacci self-fission array), A193844 (Pascal self-fission array)
Floor-sum sequence: A182653
Fractal sequences: A003602, A194029, A194832
Fractalization: A194959
Fractional parts (counts involving inequalities, intervals): A194285 A194738, A194813
Fractional parts (difference between): A194368
Fusion arrays (of polynomial sequences, infinite matrices) A193722, A202453 (Fibonacci self-fusion array), A118800 (Pascal self-fusion array)
Golden triangle: A152149, A178988, A188635
Joint-rank arrays: A184912- A184927, A182801, A182869
Jointly generated arrays (by paired polynomial recurrences): A208510
Jointly ranked sequences (with a conjecture): A206911 Kimberling expulsion array: A006852, A007963, A035486
Knight's moves on infinite chessboard: A183049
Kolakoski fan conjectures: A144586, A143589
Lagrange pairs: A210000
Matrix counts: A194508
Morphism sequences: A189576, A189628
Mysterious B-sequence (array): A186158
Natural number array: A000027, A185787
Number of diophantine solutions (w,x,y,n), etc.: A212959, A211266, A211422, A211795
Order arrays: A163254, A163255
Palindromic linear recurrences; array R(n,k) = n+[n/2]+...[n/k]: A211701
Partial complements, polygonal numbers: A086270, A086272
Partitions of the positive integers: A184812, A209423, A209489, A209082 (least power separator), A209122, A209354
Partitions of the set of positive integers (by joint rankings): A184928
Permutations of integers (conjectures): A131388- A131395
Polynomial reduction: A192175, A192232, A192744, A192951, A192872, A192904
Primes (conjectures): A184774, A185510, A174349
Prime-related arrays: A192175
Pythagorean fraction approximations: A195500
k-Pythagorean triples: A195770
Q-residues of polynomials: A193649
Rank transforms: A187224
Repetition-resistant sequence: A079101, A007061
Rules-generated sequences: A074049, A147991, A183544, A190803, A191106
Self-generating arrays: A203301, A203301
Shift-sums of zero-one sequences: A187950, A188014
Signature sequences: A084531, A007337
Symmetric matrices and interlacing roots of polynomials: A202605, A204016
Symmetric matrices and permanents: A204263, A204263, A204263, A204263
Trees generated by various sequences: A183079, A183231, A183232, A183169, A074049, A183542
Vandermonde permanents: A203468
Wythoff array: A035513, A186007, A185778
Wythoff difference array: A080164
s-Wythoff sequences: A184117
Zero-one sequences (self-generating): A188967