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Remarks: Walter Balcke appears to have been an amateur mathematician and the manufacturer of mathematical models, toys, and demonstration devices.
The following 1915 patent for a dancing figurine is affiliated with Balcke:
1,131,895 Dancing Toy Figure. Walter H. Balcke, of Winchester, Massachusetts. No execution date. Filed Nov. 2, 1914, Serial No. 869,765. Classification 40/456; 40/418; 446/302; 446/352; 446/72.
(<a href="http://www.phonozoic.net/patents/pt-1915.html" target="_blank">website</a>).
Balcke appears to have been a friend of Harvard mathematics professor J.L. Walsh, and was often invited to faculty lunches.

Walter Balcke was probably an amateur mathematician and maker of ingenious mathematical models. He gifted many such models to the Harvard Mathematics Department between 1957 and 1964. Many letters from Harvard Mathematics professors Joseph L. Walsh and Garrett Birkhoff remain. They express ongoing gratitude and appreciation for the models, and continued invitations to faculty and personal luncheons. Balcke's models were on display in the Mathematics Department at Harvard University for many years.

In the CHSI library folder (Lib 4927) one will find:

1) twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)

2) three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department

3) photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)

4) photocopy of instructional card for object 1997-1-1671

5) seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Hexagon with one side at infinity, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread

6) photograph of the display case containing Balcke's models in the Harvard Mathematics department

In the CHSI library folder (Lib 4927) one will find:

1) twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)

2) three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department

3) photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)

4) photocopy of instructional card for object 1997-1-1671

5) seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Hexagon with one side at infinity, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread

6) photograph of the display case containing Balcke's models in the Harvard Mathematics department

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