This hood belonged to to Richard Philip Baker (1866–1937) who received his PhD in mathematics from the University of Chicago in 1910. The color of the velvet on the hood represents the type of doctorate awarded, with dark blue used for the degree of Doctor of Philosophy. The color of the reverse (interior) side of the hood, maroon, represents the school that awarded the degree, i.e., the University of Chicago whose colors are maroon and white. A matching hood (1985.0820.03) was acquired by Baker’s daughter, Frances Ellen Baker (1902–1995), when she was awarded a PhD in mathematics from Chicago in 1934.
R. P. Baker’s doctoral dissertation, The Problem of the Angle-Bisectors (1985.3145.01), was directed by E. H. Moore, while his daughter Frances’s doctoral dissertation, A Contribution to the Waring Problem for Cubic Functions, was directed by L. E. Dickson, E. H. Moore’s first doctoral student. R. P. Baker’s younger daughter, Gladys Elizabeth Baker (1908-2007) earned a doctorate, in botany and mycology from Washington University in St. Louis in 1935.
R. P. Baker is best known in the mathematical community for constructing mathematical models that he believed were necessary for the proper teaching of geometry. His 1931 catalog offered several hundred models. Several museum accessions include models made by Baker. See MA.211257.04 for a description of one of these models.
This hood belonged to Frances Ellen Baker (1902–1995), who received her PhD in mathematics from the University of Chicago in 1934. The color of the velvet on the hood represents the type of doctorate awarded, with dark blue used for the degree of Doctor of Philosophy. The color of the reverse (interior) side of the hood, maroon, represents the school that awarded the degree, i.e., the University of Chicago whose colors are maroon and white. A matching hood (1985.0820.02) was awarded to Baker’s father, Richard Philip Baker (1866-1937), when he received his PhD in mathematics from Chicago in 1910.
Frances Baker’s PhD dissertation, A Contribution to the Waring Problem for Cubic Functions, was directed by L. E. Dickson, the first doctoral student of E. H. Moore, who directed her father’s PhD dissertation, The Problem of the Angle-Bisectors (1985.3145.01). Her younger sister, Gladys Elizabeth Baker (1908–2007) earned a doctorate in botany and mycology from Washington University in St. Louis in 1935.
Frances Baker spent most of her career, 1942–68, teaching mathematics at Vassar College. She came to Vassar two years after her sister Gladys arrived there to teach botany. There Frances Baker directed several honors papers and served as an officer of the local chapters of the academic honor society, Phi Beta Kappa, and the science honor society, Sigma Xi.
This geometric model was constructed by Richard P. Baker in about 1930 when he was Associate Professor of Mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over 100 of his models are in the museum collections.
The mark 411 is carved into one edge of the wooden base of this model and the typed part of a paper label on the base reads: No. 411z (/) Riemann surface : w3 = z. Model 411z is listed on page 17 of Baker’s 1931 catalogue of models as “w3 = z” under the heading Riemann Surfaces. The catalog description also notes that “411 is to serve as a first step to 412,” where Baker model 412z (211157.075) is associated with a more complicated equation involving w3.
The model represents a Riemann surface consisting of pairs of complex numbers, (z,w), for which w3 = z where a complex number is of the form x + yi for x and y real numbers and i the square root of –1. A complex plane is like the usual real Cartesian plane but with the horizontal axis representing the real part of the number and the vertical axis representing the imaginary part of the number. Riemann surfaces are named after the 19th-century German mathematician Bernhard Riemann.
Baker explains in his catalog that the z after the number of the model indicates that the metal disks above the wooden base represent copies of a disk in the complex z-plane. These disks are called the sheets of the model. The painted disk on the wooden base of the model represents a disk in the complex w-plane with the point w = 0 at its center. The disk is divided into twelve sectors, pie-piece-shaped parts of a circle centered at 0, each of which has an angle of 30 degree. The front of the model is the edge on which 411 is inscribed so the two vertical rectangles lie above the polar axis, i.e. the ray emanating from the origin when the angle is 0 degrees, of the wooden base. This places every horizontal edge of the rectangles on a polar axis of a sheet.
If z = 0, the equation w3 = z is satisfied by only one value of w, i.e., w = 0. The point z = 0 is called a branch point of the model and for all other points on the z-plane the equation w3 = z is satisfied by three distinct values of w, each of which produces a different pair on the Riemann surface (if z = 1, the three distinct pairs on the Riemann surface are (1,1), and (1,(–1 ± √3 i)/2)). Thus there are three sheets representing the same disc in the z-plane and together they represent part of what is called a branched cover of the complex z-plane.
Baker’s use of solid red circles, and dashed red and black circles indicates that each sheet is mapped continuously onto a different portion of the w-disk on the base. There are three radii of the disk on the base (the polar lines - rays emanating from the origin – for angles of 0, 120, and 240 degrees) that are the edges of sectors corresponding to quadrants on two different sheets. The order of the colors of the 30 degree sectors on the base starting at polar axis and proceeding counterclockwise correspond to the colors of the first through fourth quadrants of the top, middle, and then bottom sheets.
The vertical rectangles mentioned above are not part of the Riemann surface but call attention to what are called branch cuts of the model, i.e., curves on a sheet that produce the movement to another sheet. This movement occurs when meeting a branch cut while following a path of the inputs of z values into the equation. While the defining equation determines branch points, branch cuts are not fixed by the equation. However, the single branch cut for any surface with only one branch point must run from that point out to infinity. The branch cut of this model is represented on each sheet by the horizontal edges of the vertical surface or surfaces meeting that sheet.
In April 1981 in Springfield, Missouri, Kappa Mu Epsilon celebrated its fiftieth anniversary. At this celebration KME, a mathematics honor society with chapters at institutions that emphasize undergraduate mathematics programs, named fifty members as Distinguished Members. Sister Helen Sullivan was one of those so honored.
In about 1936 Sister Helen Sullivan organized Euclid’s Circle, a mathematics club at Mount St. Scholastica College. In 1940 she founded the Kansas Gamma Chapter of Kappa Mu Epsilon there. Sullivan often served as the faculty sponsor of her local chapter of KME, and in 1967 the alumnae of that chapter established the Sister Helen Sullivan scholarship in her honor. On the national level Sullivan served as KME’s historian in the years 1943–47, and as an assistant editor of its journal, The Pentagon, during those years and again from 1961–70.
This example of Word Puzzle belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
This puzzle was made in Hong Kong, probably in the early 1950s. It is a solitaire game known as a sliding block puzzle and looks very much like the best known sliding block puzzle, the Fifteen Puzzle, which was first described in the late nineteenth century. The aim of Fifteen Puzzle is to slide the pieces from a given starting position to get the four rows to read 1 through 15 with the blank space at the bottom right corner. Unlike the Fifteen Puzzle there is more than one solution to this Word Puzzle since the aim is to move the letters around to form as many words as possible.
In the late 19th century mathematicians proved how to determine which starting positions of the Fifteen Puzzle would lead to a solution. In particular, if the starting position in the first three rows read 1 through 12 while the fourth reads 13, 15, 14, blank, the puzzle cannot be solved. This is known as the “14-15 Puzzle of Sam Loyd” even though the puzzle author Sam Loyd first mentioned it, and challenged players to solve it, well after it had been shown to be unsolvable.
This Word Puzzle has as one of its solutions RATE YOUR MIND PAL, and for some time there were sliding block word puzzles sold showing a starting position of RATE YOUR MIND PLA to mimic Sam Loyd’s 14-15 Puzzle. However, unlike the Fifteen Puzzle, whose fifteen squares have no repetitions, this puzzle has two A’s as well as two R’s. Since the mathematical analysis of the Fifteen Puzzle implies that if there is a repetition of at least one marking on a square, then the fifteen squares can be arranged in any order you choose, this Word Puzzle can be solved either as RATE YOUR MIND PAL or RATE YOUR MIND PLA.
This paperbound book contains eighty crossword puzzles. The puzzles are almost all worked in ink, with a variety of annotations. The editor of the book was Margaret Petherbridge, and the publisher Pocket Books, Inc. A mark on the cover reads: pb (/) The POCKET BOOK of (/) CROSSWORD (/) PUZZLES (/) 100 HOURS of PUZZLE PLEASURE. A mark inked on the title page reads: #210 (/) O.C. Hazlett.
The mathematician Olive C. Hazlett once owned tne book.
For related transactions see 2015.0027 and 1998.0314.
The mathematical puzzles that belonged to the mathematician Olive C. Hazlett included these three tiny white plastic cubical dice with black spots. The faces are standard, ranging from one to six spots. The dice fit in a cylindrical metal case.
For related objects, see transactions 1998.0314 and 2015.3004.
This Japanese puzzle consists of six differently notched wooden rods that fit together to form the symmetrical object illustrated on the front of the cardboard box. The idea of wooden interlocking puzzles may have come from carpenters who made ancient wooden shrines in Japan. These shrines would not be able to withstand earthquakes with nails and glue, so wood with interlocking joints was used in place of other materials.
International interest in these puzzles began when Japan reopened to the west after being closed from the mid-seventeenth century until the mid-nineteenth century.
The box also holds a sheet of instructions.
This copy of the puzzle belonged to the mathematician Olive C. Hazlett. A mark on the lid reads: THE (/) YAMATO (/) BLOCK PUZZLE. Another mark there reads: MADE IN OCCUPIED JAPAN. After the Japanese surrender at the close of World War II, Allied forces occupied the country until the spring of 1952.
Compare MA.335284.
Reference:
Jerry Slocum and Rik van Grol, “Early Japanese Export Puzzles: 1860s to 1969s”, Puzzlers’ Tribute A Feast for the Mind, eds. David Wolfe and Tom Rodgers, Natick, Massachusetts: A K Peters, 2002, pp. 257-272.
This example of Adders, a set of four puzzles, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
Adders was made by the Douglass Novelty Company of Detroit, Michigan, and sold for ten cents. The box contains a shiny green cardboard playing board and twelve small silver cardboard discs, three blank and the others numbered 1 through 9. The directions for the four different puzzles are printed on the inside of the cover of the box. The playing board is square and has various lines and circles marked on it. Three of the four puzzles involve placing the numbered discs in specified ways so that specified sets of discs add to a given number.
Adders was probably made in about 1930, since another set of puzzles in the collections, Kangaroo (2015.0027.07), was made about then by the same company and has very similar packaging, playing board, and discs.
The first puzzle has many solutions, all of which are related to the three-by-three magic square, which is known as the Lo Shu square. That square—in which the rows, columns, and diagonals all add up to 15—appears in Chinese literature dating back to 650 BCE. Some of the solutions are equivalent to the Lo Shu square, and all the other solutions can be derived from a solution equivalent to the Lo Shu square by switching two discs, neither of which lies in the center of the circle, but are on the same line through the center of the circle.
This wire disentanglement puzzle includes three pieces that are presently linked and four additional pieces. No inscriptions on pieces. Received in cardboard box that once held thank you notes.
The pieces were once owned by mathematician Olive C. Hazlett. For related objects, see acquisitions 1998.0314 and 2015.3004.
This wire puzzle, a Chinese Nine Linked Rings Puzzle, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
There is nothing on the puzzle itself that indicates when, where, or by whom it was made.
The object of a Chinese Linked Ring Puzzle is to remove all the rings from a bar with a long slot in it. Chinese references to unlinking linked rings go back over two thousand years. Although this type of puzzle is called a Linked Ring Puzzle, the rings are not directly linked. Rather, each ring is attached to a metal wire and the ring can be removed from the bar only when that wire no longer passes through the long slot of the bar. In the early 20th century this type of puzzle was often sold with two rings that could be slipped off the bar, as in this case; the normal starting position is when only one ring can be slipped off.
Except for the ring that will be removed first, each ring has the wire of an adjacent ring going through it. All of the wires are attached to a second, often much smaller, bar from which they cannot be removed. At least two well-known European mathematicians, Girolamo Cardano (1501–1576) and John Wallis (1616–1703), unsuccessfully tried to find an analysis that would yield the smallest number of steps it would take to remove all the rings in a puzzle as a function of the number of rings. A solution to that problem was known by the late 19th century. If the starting position has only one ring that can be slipped off, a linked ring puzzle with nine rings cannot be solved in fewer than 341 steps. The mathematics involved in the analysis is related to binary reflected codes, also known as Gray codes since they were described in Frank Gray’s 1953 patent involving coding of a message signal.
This example of Dad’s Puzzler belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
This puzzle, which was copyrighted by J. W. Hayward in 1926, was manufactured by The Standard Trailer Company of Cambridge Springs, Pennsylvania. According to Around Cambridge Springs by Sharon Smith Crisman and the Cambridge Springs Historical Society, the Standard Trailer Company “originally made wagons for hauling goods” but made both Dad’s Puzzler and Ma’s Puzzle during the Great Depression (Arcadia Publishing, 2003, p. 92).
Dad’s Puzzler is a solitaire game of a type known as a sliding block puzzle. It consists of one two-by-two square, four two-by-one rectangles with the long side horizontal, two two-by-one rectangles with the long side vertical, and twoone-by-one squares. Like the best known puzzle of this type, the Fifteen Puzzle (first described in the late 19th century), the object of the game is to move blocks from one arrangement to a given final arrangement. Unlike the Fifteen Puzzle, which does not have a given starting arrangement, the starting arrangement of Dad’s Puzzler is shown on the cover of the box. Also unlike the modern Fifteen Puzzle, the blocks are not all of the same shape. Although Dad’s Puzzler blocks are not fastened to the box, the rules of the game as given on the cover of the box specify that the blocks must be moved “without jumping or raising any block from [the] bottom of the box or turning any piece.” Over the years, many versions of this puzzle have been distributed as an advertisement, often by moving companies.
The lid of the box indicates that a patent for Dad’s Puzzler had been applied for. However, in December 1907, L. W. Hardy had applied for a patent for a sliding block puzzle with the same shaped blocks as those of the later Dad’s Puzzler. The earlier patent application was for a “new and useful Improvement of Puzzle in puzzles” that stressed the number of pieces of each specific shape. These differ from those of Dad’s Puzzler, which replaced two one-by-one squares in Hardy’s version with a rectangle. The earlier patent application resulted in a patent being issued in February 1912.
Martin Gardner referred to Dad’s Puzzler in his February 1964 Mathematical Games column in the Scientific American, “The hypnotic fascination of sliding-block puzzles” (vol. 210, pp. 122–130), noting that it soon became known as Dad’s Puzzle. He also noted that the mathematical theory about which starting positions of the Fifteen Puzzle would lead to a solution did not apply to sliding block puzzles, such as Dad’s Puzzler, when the pieces were not all squares of the same size. It has since been proven that there can be no comparably simple theory that applies to all sliding block puzzles.
The following is a list, mainly of women mathematicians, of those who submitted biographical and bibliographical information about themselves to the Division of Mathematics of NMAH. Many of these women attended a 1981 meeting at the Museum that honored American women who received PhDs in mathematics prior to World War II. Others on the list later submitted the same sort of information to the division between 1981 and 1987.
Also on this list are seven male mathematicians, two of whom are fathers of women on the list and five of whom are husbands of women on the list. With the exception of Vera (Ames) Widder (1909–2004), Bryn Mawr College, 1938, all those who attended the 1981 meeting returned questionnaires. For each person listed we give name, dates of birth and death, school awarding doctorate, and year of that degree. A name in parentheses is the surname before marriage, and a number in parentheses at the end of an entry refers to a comment following the list. An asterisk before a name means that the woman attended the 1981 meeting.
*Quinn, Grace (Shover) (1906–1998), PhD, Ohio State University, 1931
Rayl, Adrienne S. (1898–1989), PhD, University of Chicago, 1939 (11)
*Reavis , Mabel (Griffin) (1907–1999), PhD, Duke University, 1933
Reschovsky, Helene J. (1907–1994), PhD, University of Vienna 1930
*Schneckenburger, Edith R. (1908–1990), PhD, University of Michigan, 1940
*Sullivan, Sister M. Helen (1907–1998), PhD, Catholic University, 1934
Tuller, Annita (1910–1994), PhD, Bryn Mawr College, 1937
Wakerling, R. K. (1914–1999), PhD, University of California, 1939 (12)
Wakerling, Virginia (Wood) (1915–1997), PhD, University of California, 1940
(1) R. P. Baker was the father of Frances E. Baker, who completed his questionnaire.
(2) Margarete D. Darkow’s questionnaire was completed by her sister, Felice E. Darkow.
(3) Orrin Frink was the husband of Aline Huke Frink.
(4) Anna M. C. Grant’s questionnaire was annotated after her death by her niece, Jessie F. Flouton.
(5) There is no questionnaire from Bella Greenfield, only a curriculum vitae.
(6) Clifton Terrell Hazard was the father of Katharine E. Hazard, who completed his questionnaire. He did not possess a PhD but was a professor of mathematics at Purdue University.
(7) Ernest A. Hedberg was the husband of Marguerite Zeigel Hedberg, who completed his questionnaire.
(8) Ralph E. Huston was the husband of Antoinette Killen Huston, who completed his questionnaire.
(9) A. J. Maria was the husband of May Hickey Maria, who completed his questionnaire.
(10) There is no questionnaire from Joanna Isabel Mayer, only correspondence.
(11) Adrienne S. Rayl submitted a questionnaire completed with the assistance of her nephew, Donald R. Wilken.
(12) R. K. Wakerling was the husband of Virginia W. Wakerling.
The book Mathematical Puzzles and Pastimes was obtained by Olive C. Hazlett (1890–1974) on May 27, 1965. Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This volume, as well as other puzzle books and puzzles she owned, was collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
The puzzles and pastimes of the book were gathered and edited by Philip Haber and illustrated by Stanley Wyatt. The book was published by The Peter Pauper Press of Mount Vernon, New York, in 1957. Haber collected problems that he wrote could “be solved primarily by clear thinking, arithmetic or algebra.” The book contains 113 problems with solutions given to some of them. Haber refers to the last four problems as “famous” and gives their names as: The Impossible Division Problem, The Unit Problem, The Apple Problem, and The Problem of Problems (Archimedes’ Cattle Problem).
Hazlett wrote “$1. for 3” on the title page of this book. There is one other book in the museum collections, The Little Riddle Book (2015.3004.02), that was also published by The Peter Pauper Press and also obtained by Hazlett on May 27, 1965. In that book she wrote “3 for $1.” Hazlett signed her name “O. C. Hazlett” on the dustcover of both books. She made other handwritten marks in Mathematical Puzzles and Pastimes, including several whose meanings are not clear.
The mathematical puzzles that belonged to the mathematician Olive C. Hazlett included these six translucent plastic die. Three are green and three red. All have the standard faces, ranging from one to six white spots.
For related objects, see transactions 1998.0314 and 2015.3004.
This example of Mystery Maze belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
On the back of this puzzle there are marks that indicate that it was manufactured by the Harmonic Reed Corporation of Philadelphia, Pennsylvania, and that a patent had been applied for. The following description of the puzzle appears in the February 3, 1951, issue of The Billboard: The Amusement Industry’s Leading Newsweekly on page 66 under Merchandise Topics: “To retail for 50 cents, Harmonic Reed Corporation has introduced its Mystery Maze puzzle. The plastic tilt puzzle, with clear top and standard beebee ball, has the unusual feature of a concealed section. Though unseen by the player, the ball must pass thru this section to reach the finish. However, if a mistake is made, the ball will not go farther and must be returned to the puzzle’s starting point before another try at the concealed section can be made.”
This cloth-bound book was imported from England and given to Robert Hazlett (the father of mathematician Olive C. Hazlett) by his father in 1882. The author of the book was "One of the Old Boys" and it was published by "Hand and Heart" Publishing Office. The preface is by the Rev, Charles Bullock, B.D.
For related transactions see 2015.0027 and 1998.0314.
This set of game pieces is for a game of Chinese checkers. A cardboard box divided into three sections holds fifteen red, fifteen yellow, and fifteen green wooden pieces. The box also holds a booklet of instructions.
A mark on the lid of the box reads: Ching Gong (/) ORIENTAL CHECKERS (/) [. . .] SAML. GABRIEL SONS & COMPANY - NEW YORK MADE IN U. S. A. No. 99. The term "Ching Gong oriental checkers" was trademarked by Samuel Gabriel Sons & Company November 23, 1935.
Another mark on the lid reads: O.C. Hazlett. This is the signature of the mathematician Olive C. Hazlett.
This solitaire game consists of a round transparent plastic case holding a white plastic pegboard and thirty-three red plastic pegs. The thirty-three holes in the board are arranged as in English peg solitare. Instructions are in the case, visible through the bottom.
A mark on the lid of the case reads: "YOGO" (/) JUMP-a-PEG (/) PUZZLE. Another mark on the lid reads: BROOKLYN NY (/) PLAS-TRIX.
The mathematician Olive C. Hazlett once owned this game.
For an account of a similar object, see The Jerry Slocum Mechanical Puzzle Collection, Lilly Library, Indiana University, object 11226.
According to advertisements and articles in the New York Times, Plas-Trix Company was in business in Brooklyn by 1950 and went bankrupt in 1960.
Reference:
John D. Beasley, The Ins and Outs of Peg Solitaire, Oxford: Oxford University Press,1985.