#
Women Mathematicians and NMAH CollectionsOlive C. Hazlett: Music and Puzzles

Olive C. Hazlett. Photograph courtesy of LHM Institute. (AHB2012q06024) |

Olive Clio Hazlett (1890-1974)** **was a leading American mathematician of the 1920s. She was the most prolific of the US-born women of her time who worked in pure mathematics and was recognized for her research accomplishments when, in 1927, she became the second US-born woman to be ranked as one of American’s leading mathematicians by her peers, a distinction marked by a “star” in *American Men of Science.* In 1984, Hazlett was one of three mathematicians whose lives were celebrated in an exhibit NMAH.

Hazlett, who was awarded a PhD in mathematics from the University of Chicago in 1915, spent a postdoctoral year at Harvard University before she began her teaching career at Bryn Mawr. In 1918 she moved to Mount Holyoke and seven years later she moved to the University of Illinois.

As with most people, mathematicians have interests outside their profession. Among mathematicians, including Hazlett, these outside interests often relate to music and puzzles. Among objects in the collections that were displayed in 1984 are her tenor recorder, a set of dominoes with more spots than one sees on most domino sets, and twelve Japanese interlocking wooden puzzles called “Kumiki.”

“Commemorating American Mathematics,” 1984 Exhibit at NMAH. (SI Neg #84-5347-2) |

"Women Mathematicians and NMAH Collections - Olive C. Hazlett: Music and Puzzles" showing 2 items.

## The Embossing Company's Double Twelve Express Dominoes

- Description
- This set of Double Twelve Express Dominoes was made by the Embossing Company, an Albany, N.Y., firm that produced wooden blocks and puzzles. A sheet of instructions, “HOW TO PLAY DOMINOES,” is included in the box of ninety-six rectangular tiles. Five of these are completely blank and ninety-one are made up of two squares with each square either blank or marked with up to 12 spots, usually called pips.

- The traditional American domino set is called Double Six, because each rectangular tile is made up of two squares with each square blank or marked with 1, 2, 3, 4, 5, or 6 pips. In a Double Six set, one can see seven different types of tile depending on the smallest number of pips in one of its squares. If the smallest number of pips is 0, at least one square is blank and there are seven possibilities for the number of pips in the other square, i.e., 0 through 6. If the smallest number of pips is 1, neither square is blank and at least one square has a single pip. In this case there are six possibilities for the number of pips in the other square, i.e., 1 through 6. In general when the smallest number of pips that appear on a square of a tile is
*k*, the other square must have*k*,*k*+1, …, 6 pips on it, and it is always the case that there are 7-*k*numbers on the list*k*,*k*+1, …, 6. If we look at all be seven possible types of tiles in a Double Six set, we find that there are 7+6+5+4+3+2+1=28 tiles.

- A similar computation can be done for any Double
*n*set of dominoes. I.e., there are*n*+1 tiles with one or both squares blank,*n*tiles with no blanks and 1 the smallest number of pips, and*n*+1-*k*tiles with no blanks and*k*the smallest number of pips. This leads to a total of (*n*+1)+*n*+(*n*-1)+…+1 tiles, i.e., the sum of the first*n*+1 integers. A mathematical formula known for many centuries says that the sum of the first*n*integers is*n*(*n*+1)/2 so the sum of the first*n*+1 integers is (*n*+1)(*n*+2)/2. For a set of Double Six dominoes*n*+1 is 7 so we get (7)(8)/2 or 28 tiles. Other common Double*n*sets include Double Nine, Double Twelve, Double Fifteen, and Double Eighteen. For the Double Twelve set,*n*+1 is 13 so there are (13)(14)/2 or 91 tiles. In order not to leave empty space in the box, five completely blank tiles were included in this set of Double Twelve dominoes.

- These dominoes belonged to Olive C. Hazlett (1890–1974), one of America's leading mathematicians during the 1920s. Hazlett taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, N.H. Her set of dominoes was collected from the Carmelite community of Leadore, Idaho. Brothers from this community who had lived in New Hampshire had befriended Hazlett there.

- Location
- Currently not on view

- maker
- Embossing Company

- ID Number
- 1998.0314.01

- accession number
- 1998.0314

- catalog number
- 1998.0314.01

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Wooden Puzzle Assortment

- Description
- These twelve interlocking three-dimensional wooden puzzles were made in Japan, likely by the Yamanaka Kumiki Works. Each is individually wrapped in plastic and includes a sheet showing how to assemble it. A trademark on the bottom of the box includes an image of a globe surrounded by the letters T T N Y. According a 1978 application to the US Patent and Trademark Office by the Traveler Trading Company, Inc., the mark was first used in commerce in 1950. Since imports from Japan between 1945 and 1952 had to be labeled “Made in occupied Japan” and the labels on the box, the puzzles, and the instructions, all read “Made in Japan,” these puzzles were imported into the United States some time after 1952.

- These types of Japanese puzzles are called “kumiki” and are said to be related to the traditional construction of wooden buildings that did not use nails or glue. This particular set includes four familiar geometrical shapes (a sphere, a cube, a barrel, and an octagonal prism), four animals (an elephant, a pig, a bird, and a dog), and four shapes without common names. Only the dog and one of the unnamed shapes are unassembled.

- These kumiki puzzles belonged to Olive C. Hazlett (1890–1974), one of America's leading mathematicians during the 1920s. Hazlett taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. The puzzles were collected from the Carmelite community of Leadore, Idaho. Brothers from this community had lived in New Hampshire earlier, and befriended Hazlett there.

- REFERENCE: Jerry Slocum and Rik van Grol, “Early Japanese Export Puzzles: 1860s to 1960s,” in
*Puzzlers’ Tribute: A Feast for the Mind*, eds. David Wolfe and Tom Rodgers (Natick, MA: A. K. Peters, 2002): pp. 257-71.

- Location
- Currently not on view

- date made
- ca 1955

- ID Number
- 1998.0314.02

- accession number
- 1998.0314

- catalog number
- 1998.0314.02

- Data Source
- National Museum of American History, Kenneth E. Behring Center