Geometric Models - Models by Richard P. Baker

Around 1900, mathematicians across the world acquired physical models, both to illustrate concepts they taught and to demonstrate their familiarity with new ideas. They frequently purchased models from Europe, especially Germany. A few Americans also designed and made models. One of them was English-born Richard P. Baker (1866-1937), who began making models while he was a graduate student at the University of Chicago, publishing his first list of 100 models in 1905. These objects largely followed contemporary textbooks. By 1931. Baker was a professor of mathematics at the University of Iowa, and he had designed over 500 models, many on more abstract topics. Somme models were less expensive copies of those made in Germany. Baker’s designs also included surfaces associated with areas of physics such as thermodynamics, optics, and mechanics

Baker sold models to the University of Delaware, and a variety of other colleges and universities. After his death, his daughters sold part of his remaining stock to the University of Arizona, where it remains to this day. They also placed over one hundred models on exhibition at MIT, where they stayed from the late 1930s until 1956. From there, they came to the Smithsonian. A few other models in Baker’s style were given to the museum by Brown University, and are also included here.

Baker carefully numbered the designs for his models, and labeled examples with title and number. The objects shown here are in the order he assigned them, where this is known. Another dozen models have no number, and are listed afterward. Finally, the object group includes biographical materials relating to Baker and his career.

Showing 1 to 24 of 138 items — page 1 of 6

Model for Desargues' Theorem with Triangles in Different Planes, by Richard P. Baker, Baker #49a

This metal model was constructed by Richard P. Baker. A mathematics professor at the University of Iowa, Baker believed that models were essential instruction in many parts of mathematics and physics.
Description
This metal model was constructed by Richard P. Baker. A mathematics professor at the University of Iowa, Baker believed that models were essential instruction in many parts of mathematics and physics. Over one hundred of his models are in the NMAH collections.
The painted wire structure is a model for Desargues' Theorem. A paper tag reads: No. 49a Desagues' Theorem by (/) projection (/) Triangles in different (/) planes. This version of the model is not listed in Baker's 1905 catalog, but is included in the 1931 catalog. The model sold for $2.50.
References:
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 13.
Richard P. Baker Papers, University Archives, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1900-1935
ca 1910-1935
maker
Baker, Richard P.
ID Number
MA.211257.001
accession number
211257
catalog number
211257.001

Model of a Twisted Cubic by Richard P. Baker, Baker #72 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.
A typed paper label on the top of the wooden base of this model reads: No. 72 (/) TWISTED CUBIC (/) (by cone and cylinder).
Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. The two ruled surfaces shown here are a cylinder, indicated with red threads, and a double cone, indicated in yellow. The points where the surfaces intersect are highlighted with a wire. This curve of intersection is of degree three and is known as a twisted cubic.
The model sold for $4.00.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 13.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72.
R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
George Salmon, A Treatise on the Analytic Geometry of Three Dimensions, Dublin: Hodges, Foster, and Company, 1874, esp. pp. 303-313.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.002
accession number
211257
catalog number
211257.002

Model of a Twisted Cubic by Richard P. Baker, Baker #74 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.
A typed paper label on the top of the wooden base of this model reads: No. 74 (/) TWISTED CUBIC: 3 real (/) asymptotes.
Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of three hyperbolic cylinders, one with yellow strings, one with blue strings, and one with red strings (a hyperbolic cylinder is a surface that joins two parallel hyperbolas, just as a regular cylinder joins two parallel circles. For a model, see 1982.0795.33). The hyperbolic cylinders in this model all make an acute angle with the base. Three pieces of wire indicate places where the three hyperbolic cylinders intersect. These are part of a curve of degree three known as a twisted cubic, in this case a twisted cubic with three real asymptotes.
The model sold for $7.50.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 13.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72. R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
George Salmon, A Treatise on the Analytic Geometry of Three Dimensions, Dublin: Hodges, Foster, and Company, 1874, esp. pp. 303-313.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.003
accession number
211257
catalog number
211257.003

Model of a Twisted Cubic by Richard P. Baker, Baker #75 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.
A typed paper label on the top of the wooden base of this model reads: No. 75 (/) CUBICAL HYPERBOLIC PARABOLA.
Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of a parabolic cylinder (going crosswise) and a hyperbolic cylinder (with two opposite sections, extending vertically). One asymptotic plane of the hyperbolic cylinder is parallel to what Sommerville calls the axial plane of the parabolic cylinder. The cylinders intersect in two curves which are represented by wires in the model. These wires are part of a cubical hyperbolic parabola.
The model sold for $5.00.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 13.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72. R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
George Salmon, A Treatise on the Analytic Geometry of Three Dimensions, Dublin: Hodges, Foster, and Company, 1874, esp. pp. 303-313.
D. M. Y. Sommerville, Analytical Geometry of Three Dimensions, Cambridge: Cambridge University Press, 1959, esp. pp. 294-297.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.004
accession number
211257
catalog number
211257.004

Model of a Cubical Parabola by Richard P. Baker, Baker #76 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.
A typed paper label on the top of the wooden base of this model reads: No. 76 (/) TWISTED CUBIC: CUBICAL (/) PARABOLA. A mark incised in the base at the front reads: 76 R.P.B.
Like several other models Baker made, this shows ruled surfaces, also called scrolls. Such a surface is swept out by a moving line. This model shows portions of a parabolic cylinder (going crosswise with blue strings) and a hyperbolic paraboloid (in red strings). A metal wire along the points of intersection indicates the cubical parabola.
The model sold for $5.00.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 13.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72. R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
George Salmon, A Treatise on the Analytic Geometry of Three Dimensions, Dublin: Hodges, Foster, and Company, 1874, esp. pp. 303-313.
D. M. Y. Sommerville, Analytical Geometry of Three Dimensions, Cambridge: Cambridge University Press, 1959, esp. pp. 294-297.
Website of the University of Arizona Mathematics Department, accessed June 22, 2017.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.005
accession number
211257
catalog number
211257.005

Model of a Cubic Cone with Nodal Line by Richard P. Baker, Baker #78 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the bottom of the wooden base of this model reads: No. 78 (/) CUBIC CONE WITH NODAL LINE. Model 78 appears on page 7 of Baker’s 1931 catalog of models as “With nodal line” under the heading Cubic Cones . It also appears in his 1905 catalog of one hundred models.
Baker’s string models always represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows two ruled surfaces. One of these surfaces is swept out by any of the threads connecting the curved vertical wooden sides of the model. The other ruled surface is swept out by any of the threads joining the curved horizontal piece of wood on the top of the model to the wooden base of the model. All the threads of this model pass through a point in the center of the model, which is the intersection of two special lines, one for each ruled surface.
The special line for the surface joining the vertical sides is the line connecting the inflection points of the cubic curves, i.e. the points where the curve changes from concave upward to concave downward (for the curve y=x3, it would be at the origin). This line is horizontal and passes over the center of the base.
The special line for the other curve is the vertical line going through the center of the base. It is formed by connecting the point where the upper curve crosses itself with the center of the base, which is also the point where the curve on the base crosses itself. A point of curve where the curve crosses itself is called a node, so all points of this vertical line are nodes and this is the nodal line of the surface.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.006
accession number
211257
catalog number
211257.006

Model of Cubic Cones with a Cuspidal Edge by Richard P. Baker, Baker #81 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the top edge of the wooden frame of this model reads: No. 81 (/) CUBIC CONE: (/) CUSPIDAL EDGE.
Baker’s string models represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows the ruled surface swept out by the yellow threads connecting the sides, base, and top of the model.
A version of the model sold for $4.50, but it may have been considerably smaller.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 14.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 7.
R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.007
accession number
211257
catalog number
211257.007

Model of a Cubic Cone Showing Only a Single Sheet by Richard P. Baker, Baker #82 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the bottom of the wooden base of this model reads: No. 82 (/) cubic cone: SINGLE SHEET (/) only.
Baker’s string models represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows the ruled surface swept out by the yellow threads connecting the curved vertical wooden sides of the model and by the threads joining the curved horizontal piece of wood on the top of the model to the curved piece at the front. All the threads of this model pass through a point in the center of the model which intersects a wire rising from the base.
The model sold for $4.50.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 14.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 7.
R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.008
accession number
211257
catalog number
211257.008

Model of a Cylindroid by Richard P. Baker, Baker #83 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections. Baker mentioned the model in a 1905 listing of one hundred models he had constructed as well as in a 1931 catalog.
A typed paper label on the top of the wooden base of this model reads: No. 83 (/) CYLINDROID.
Like several other models Baker made, this shows a ruled surface, also called a scroll. Such a surface is swept out by a moving line. This line is represented by the blue string in the model. The string rotates periodically about the vertical access, and at the same time moves uniformly up (or down) the vertical axis. The surface also is known as Plücker’s conoid after the German mathematician and physicist Julius Plücker.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 13.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 72.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.009
accession number
211257
catalog number
211257.009

Model of a Quartic Scroll by Richard P. Baker, Baker #84 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905, when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905, when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the wooden base of this model reads: No. 84 Quartic Scroll, (/) with two nodal straight (/) lines. Model 84 appears on page 8 of Baker’s 1931 catalog of models as “Quartic Scroll , with two nodal straight lines.” The equation of the model is listed as (x2/((z - 1) 2)) + (y2/((z + 1) 2)) = 1. It also appears in his 1905 catalog of one hundred models.
Baker’s string models always represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model is swept out by any of the yellow threads joining the elliptically shaped horizontal piece of wood on the top of the model to the wooden base of the model.
In addition to the yellow threads of the model, there are two horizontal red threads that run from the rods at near the edge of the base and are parallel to the lines connecting the midpoints of the opposite sides of the square of surface of the base. There is a segment of each of these red threads for which each point meets two different lines of the model and the points of these segments are called double points, or nodes, of the surface. Thus these line segments are the two nodal lines of the model. The horizontal plane z = 1 intersects the model at the upper horizontal thread, while the horizontal plane z = -1 intersects it at the lower horizontal thread. When z=1, the points of intersection are (0,y,1) for y between -2 and 2. When z=-1, the points of intersection are (x,0,-1) for x between -2 and 2. Thus the nodal lines are the line segments connecting (0,-2,1) to (0,2,1) and (-2,0,-1) to (2,0,-1).
When z = 0 the equation of the surface becomes x2 + y2 = 1, so the horizontal plane z = 0 intersects the model at the unit circle with center at the origin. For any other value of z, the equation of the surface is of the form (x2/a2) + (y2/b2) = 1, where a does not equal b. This is the standard form for the equation of an ellipse.
Location
Currently not on view
date made
ca 1915-1935
ca 1905-1935
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.010
accession number
211257
catalog number
211257.010

Model of a Scroll of Order Eight by Richard P. Baker, Baker #85 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the bottom of the wooden base of this model reads: No. 85 (/) SCROLL OF ORDER 8 (/) CONES WITH COMMON VERTEX.
Baker’s string models represent a special type of geometric surface called a ruled surface. A ruled surface, sometimes called a scroll, is one that is swept out by a moving line. This model shows the ruled surfaces generated by the double tangents of two spheres through a line. The two spheres are white balls with diameters of three inches and 1 ½ inches (7.6 cm. and 3.8 cm.). The tangent lines are in blue thread – each thread is tangent to both spheres and passes through the line shown in yellow thread. According to Baker’s label and catalogs, the surface is of degree eight.
The model sold for $8.00.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 14.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 8.
R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.011
accession number
211257
catalog number
211257.011

Model of the Differential Geometry of a Helix by Richard P. Baker, Baker #89 (a Ruled Surface)

This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa.
Description
This string model was constructed by Richard P. Baker, possibly before 1905 when he joined the mathematics faculty at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the top of the wooden base of this model reads: No. 89 (/) Diff. Geometry of a helix. The model illustrates several terms used to describe curves in three-dimensional space, using as an example the spiral curve on a cylinder known as a helix. In the model, the cylinder is represented by blue threads and the helix by a wire that twists along it. The point of interest, hereafter called P, is at the center, atop a wire extending perpendicularly from the base (the normal to the helix at the point). Shown with red threads is the osculating (kissing) plane to the helix at P. The red thread that passes through P represents the tangent line at P. The wire circular arc passing through P in the osculating plane represents part of what is called the osculating circle. The smaller circles joined by wires that pass through P form what is called the osculating cone.
Shown with yellow threads is a plane perpendicular to the osculating plane known as the normal plane. The thread on this plane that passes through P is called the binormal to the curve at P.
The model sold for $7.50.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 16.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 12.
R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.012
accession number
211257
catalog number
211257.012

Model of Lines of Curvature on an Ellipsoid by Richard P. Baker, Baker #90

This is a model of lines of curvature on an ellipsoid. The rectangular wooden base supports a plaster half-ellipsoid with grid of ellipses drawn on it. A tag on the model reads: No. 90 (/) LINES OF CURVATURE ON (/) ELLIPSOID.References:R. P.
Description
This is a model of lines of curvature on an ellipsoid. The rectangular wooden base supports a plaster half-ellipsoid with grid of ellipses drawn on it. A tag on the model reads: No. 90 (/) LINES OF CURVATURE ON (/) ELLIPSOID.
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 16. A copy of this document is in the Baker Papers at the University of Iowa Archives.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 12.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.013
accession number
211257
catalog number
211257.013

Model of Contour Lines by Richard P. Baker, Baker #92

This painted plaster model showing contour lines fits in an open wooden box.In a catalog from about 1905, Baker described the surface shown as “a quasi geographical [sic] area containing 3 peaks, 1 hollow, and 2 passes. Contours, slope lines, ridge, and course lines are marked.
Description
This painted plaster model showing contour lines fits in an open wooden box.
In a catalog from about 1905, Baker described the surface shown as “a quasi geographical [sic] area containing 3 peaks, 1 hollow, and 2 passes. Contours, slope lines, ridge, and course lines are marked. An inloop and outloop curve occur.”
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 16. A copy of this document is in the Baker Papers at the University of Iowa Archives.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 5.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.014
accession number
211257
catalog number
211257.014

Model of Contour Lines by Richard P. Baker, Baker #93

This painted plaster model showing contour lines fits in an open wooden box.In a catalog from about 1905, Baker described the surface shown as “An area which can be derived by deformation from 92 [e.g.
Description
This painted plaster model showing contour lines fits in an open wooden box.
In a catalog from about 1905, Baker described the surface shown as “An area which can be derived by deformation from 92 [e.g. model MA.211257.014] without losing the descriptive character of contours, except that the inloop curve becomes an outloop (which may occur in infinitesimal transformation). The contours are now curves of the type of equipotential lines, and the configuration is made as symmetrical as possible.”
References:
R. P. Baker, A List of Mathematical Models, [1905], p. 16. A copy of this document is in the Baker Papers at the University of Iowa Archives.
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 5.
Location
Currently not on view
date made
ca 1900-1935
maker
Baker, Richard P.
ID Number
MA.211257.015
accession number
211257
catalog number
211257.015

Model for Projective Geometry by Richard P. Baker, Baker #103

This painted wire structure is a model for projective geometry. It shows four points projected to four points in different planes. A typed paper tag attached to one edge reads: No. 103 (/) 4 pts. to 4 pts. in diff. (/) planes.
Description
This painted wire structure is a model for projective geometry. It shows four points projected to four points in different planes. A typed paper tag attached to one edge reads: No. 103 (/) 4 pts. to 4 pts. in diff. (/) planes. This is one of a series of models for projective geometry listed in Baker’s 1931 catalog. It sold for $5.00.
Reference:
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 13.
Richard P. Baker Papers, University Archives, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1900-1935
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.016
accession number
211257
catalog number
211257.016

Model of a Rhombic Dodecahedron by Richard P. Baker, Baker #110

This is a wire skeleton model of a rhombic dodecahedron, a twelve-sided figure whose faces are rhombuses.. A typed paper tag reads: No. 110 (/) RHOMBIC DODECAHEDRON.Reference:R. P. Baker, Mathematical Models, Iowa City, Iowa,1931, p. 5.Currently not on view
Description
This is a wire skeleton model of a rhombic dodecahedron, a twelve-sided figure whose faces are rhombuses.. A typed paper tag reads: No. 110 (/) RHOMBIC DODECAHEDRON.
Reference:
R. P. Baker, Mathematical Models, Iowa City, Iowa,1931, p. 5.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.017
accession number
211257
catalog number
211257.017

Model of Translation by Two Reflections in a Line, by Richard P. Baker, Baker #116

This geometric model was constructed by Richard P. Baker in the early twentieth century when he was Associate Professor of Mathematics at the University of Iowa.
Description
This geometric model was constructed by Richard P. Baker in the early twentieth century 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.
This is one of several models Baker made that relate to projective geometry. More specifically, he wrote in the catalog of his models: “In Lie’s analysis of projective transformation occur eight elements. Illustrations of their composition, mostly intuitive, are:-.” Baker then listed the models to which he assigned numbers 115 through 128. This, apparently the only one of the set in the Smithsonian collections, is number 116, which Baker describes as “Translation by two reflexions in a line.”
The model is made of metal and includes three heavy wires with arrows on the ends. The longest arrow is painted blue on top and is not firmly attached to the model. The red and white arrows meet and are perpendicular to each other. They are also both are attached to a flat white metal piece that is roughly elliptical in shape. There is a blue metal surface in the shape of a cone through which the white surface passes. A mark in pencil reads: 116. This model does not have a typed paper label like others Baker used to indicate the title and number of the model.
Two loose pieces that may be associated with this model were noted by museum intern Kristin Haring in the 1990s. One consists of wires that closely resemble the arrows of the model except that the red arrow runs much closer to the blue section of the long arrow and there is a thinner wire with an ending that is shaped differently than an arrow. The second piece is the same as the thinner wire that was added to the wires of the model to form the first piece.
Because it is not clear what Baker’s model number 116 originally looked like, a full interpretation is not attempted. According to the accession file, a copy of model 116 (but no other models in the range 115 to 128) was sent by Baker’s descendants for exhibition at MIT in 1939 and later came to the Smithsonian.
References:
Richard P. Baker, Mathematical Models, Iowa City, 1931, pp. 14-15.
Accession file.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.018
accession number
211257
catalog number
211257.018

Model of a Twisted Polygon by Richard P. Baker, Baker #131

A twisted polygon is a closed broken line whose sides do not all lie in the same plane. This model of such a figure is made from painted 1/8 inch steel wire. The range is over a quarter of a circle.
Description
A twisted polygon is a closed broken line whose sides do not all lie in the same plane. This model of such a figure is made from painted 1/8 inch steel wire. The range is over a quarter of a circle. According to Baker’s catalog description, the model includes “osculating and normal planes and polar lines in penultimate position.” The penultimate position is the one next to the rightmost in the image, the osculating plane is represented by two short wires, and the normal plane at this point is indicated by lower wires approaching the pole at the back.
A paper tag reads: No. 131 (/) Twisted polygon: diff. geom.
The model sold for $2.50.
References:
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 11.
Richard P. Baker Papers, University Archives, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.019
accession number
211257
catalog number
211257.019

Model of a Twisted Polygon by Richard P. Baker, Baker #133

A twisted polygon is a closed broken line whose sides do not all lie in the same plane. This model shows a few sides of such a polygon, namely the edges ABCDE. All lie on a double cone, which also is shown.
Description
A twisted polygon is a closed broken line whose sides do not all lie in the same plane. This model shows a few sides of such a polygon, namely the edges ABCDE. All lie on a double cone, which also is shown. The sides BC and CD lie in one plane, which is represented by a large circle that intersects the cone. The sides CD and DE lie in a second plane, represented by another large circle. The sides AB and BC lie in a third plane, represented by a quadrilateral tangent to the cone. A plane perpendicular to CD at its midpoint also is represented by a circular wedge. Baker described this model as showing “osculating planes and cone with center of spherical curvature.”
The model sold for $2.50.
References:
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 11.
Richard P. Baker Papers, University Archives, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.020
accession number
211257
catalog number
211257.020

Model of the Locus of Spherical Curvature of a Screw by Richard P. Baker, Baker #134 (a Ruled Surface)

This string model was constructed by Richard P. Baker after he joined the mathematics faculty at the University of Iowa in 1905.
Description
This string model was constructed by Richard P. Baker after he joined the mathematics faculty at the University of Iowa in 1905. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.
The typed part of a paper label on the top of the wooden base of this model reads: No. 134 (/) Screw: locus of spherical (/) curvature. Model 134 is listed in Baker’s 1931 catalog as a model for differential geometry with the title shown. No dimensions are given.
The planes, line segments, cone, cylinder and helix shown in this model are identical to those of Baker’s model 89 (MA.211257.012), although the color of the thread is different.
The model reportedly sold for $5.00.
References:
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 11.
R. P. Baker Papers, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.021
accession number
211257
catalog number
211257.021

Model of a Twisted Polygon by Richard P. Baker, Baker #135

A twisted polygon is a closed broken line whose sides do not all lie in the same plane. This model shows four edges of such a polygon.
Description
A twisted polygon is a closed broken line whose sides do not all lie in the same plane. This model shows four edges of such a polygon. For the three edges in the center of the model, a line segment perpendicular to two adjacent edges is indicated (these are binormals of the polygon at the point). The back of the model contains three quadrilaterals that contain two adjacent edges of the twisted polygon (that is to say, that represent part of three osculating planes of the polygon). It also contains two triangles representing planes normal to edges of the polygon at their midpoints (representing normal planes).
According to Baker’s catalog description, the model represented “osculating, normal and rectifying planes, rectifying lines” for a twisted polygon. The model sold for $2.00.
The model is presently in two pieces.
References:
R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 11.
Richard P. Baker Papers, University Archives, University of Iowa, Iowa City, Iowa.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
ID Number
MA.211257.022
accession number
211257
catalog number
211257.022

Model of Surface of Binormals to a Twisted Cubic by Richard P. Baker, Baker #139 (a Ruled Surface)

This geometric model was constructed by Richard P. Baker in the early twentieth century when he was Associate Professor of Mathematics at the University of Iowa.
Description
This geometric model was constructed by Richard P. Baker in the early twentieth century 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.
A typed paper tag glued to the base of the model reads: No. 139 (/) SURFACE OF BINORMALS TO (/) TW. CUBIC THREAD. This is one of four models in the museum collections that Baker listed in a section, “A Study of the Twisted Cubic,” of his 1931 catalog (see also MA.211257.024, MA.211257.025, and MA.211257.30).
A twisted cubic is so called because it does not lie in any plane in three space and is often represented by the vector function of t: (t, t2, t3). The notation Baker used in computing the surface of binormals is the same as appears in a 1909 book, A Treatise on the Differential Geometry of Curves and Surfaces, by the American mathematician Luther Eisenhart. In this model the copper wire that runs from one side of the wooden base to the opposite side represents a twisted cubic.
The binormals to this curve are represented by the yellow threads, which means that the threads meet the curve where they are perpendicular to the osculating plane. The term osculating derives from the Latin for kissing and in three-dimensional geometry mathematicians use the term to refer to the plane formed by the tangent and normal vectors at the point.
Reference:
John B. Little, “The Many Lives of the Twisted Cubic,” The American Mathematical Monthly, 126 (2019) no. 7, pp. 579-592.
Location
Currently not on view
date made
ca 1906-1935
Associated Date
ca. 1905-1931
maker
Baker, Richard P.
ID Number
MA.211257.023
accession number
211257
catalog number
211257.023

Model of the Surface of Tangents to a Twisted Cubic by Richard P. Baker, Baker #140 (a Ruled Surface)

This geometric model was constructed by Richard P. Baker in the early twentieth century when he was Associate Professor of Mathematics at the University of Iowa.
Description
This geometric model was constructed by Richard P. Baker in the early twentieth century 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.
When the model was constructed there was probably a copper wire representing a twisted cubic, a smooth curve in three dimensions so that each of the three variables is represented as a polynomial in a fourth variable and each of these polynomials is of degree at most three with at least one of the three a cubic polynomial. Since the blue threads represent the lines that are tangent to that, now missing, curve, the wire representing it probably ran from pieces of wood attached to the wooden base as seen on the left and right sides of the model in image NMAH-DOR2013-18269. That placement would make the twisted cubic have a shape similar to the copper wire seen in MA.211257.023.
Location
Currently not on view
date made
ca 1906-1935
maker
Baker, Richard P.
Baker, Richard P.
ID Number
MA.211257.024
accession number
211257
catalog number
211257.024

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