*William Hugh Kenner* (January 7, 1923 – November 24, 2003), was a Canadian literary scholar, critic and professor. Kenner was unusual in that he bridged the gap between the humanities and the sciences: his made significant contributions both to modernist literature theory and engineering. His books include an appreciation of Chuck Jones the creator and animator of Bugs Bunny and Road Runner, arguing that Jones had invented an art that was as precise and technical as any other; an appreciation of Buckminster Fuller, and a user's guide for the Heath/Zenith Z-100 computer; in his later years was a columnist for both Art & Antiques and Byte magazine.

Of interest to tensegrity researchers is Kenner's book on geodesic math.

Geodesic Math and How to use It

Printed in 1976 and reprinted since, Kenner's text was the first, and remains a cogent, overview of the mathematics of tensegrity and geodesic structures.

Kenner took the position that geodesics are a special case of tensegrity structure. He wrote in the preface, "Fuller's geodesic domes constitute a special case of a larger class of Fuller constructs called Tensegrities, and the way to an intuitive understanding of domes is to understand Tensegrity first." Following this approach, part one of the book is about tensegrity mathematics, divided into six chapters of (1) weight vs. tension, (2) spherical tensegrities, (3) complex spherical tensegrities, (4) tendon system minima, (5) geodesic subdivision and (6) rigid tenesegrities.

Appendices contain data lookup tables, and programming code for the HP-65 calculator.

Kenner hints that Fuller invented tensegrity, but it was co-invented by Snelson, Emmerich and others.

While Kenner states the mathematical prerequisites for understanding the book as 'algebra and high-school trig' the tensegrity part of the book requires an understanding of some differential calculus.

In Chapter 1, at the end of the appendix Kenner claims that there are no regular t-prisms beyond 3, 4 and 5. This is incorrect, see Burkhardt's 6 prism

In Chapter 2, the first sentence should not use the term rhomboidal. Burkhardt corrects it to read. "The three-strut Tensegrity described in Chapter 1 is asymmetrical, having triangular ends and folded rhomboids for sides."

Kenner's treatment of the "symmetrical 6-strut Tensegrity" is confusing. Fuller, who developed this structure in 1949, called it a tensegrity icosahedron.

In Chapter 3, at the bottom of p. 20, Diagram 3.1 should say the equator, the Greenwich meridian, and the 90° meridian.

Chapter 3's Table 3.1 and appendix has errors, updated on Burkhardt's site.

Chapter 5's inventory of the triangles in Diagram 5.8 is missing a fifth shape, namely the three isosceles BCC triangles.

"Chapter 6 ('Rigid Tensegrities') uses the so-called (by others, not by Kenner) deresonated tensegrity spheres to make a connection between tensegrity structures and geodesics. While I think deresonated structures and their rotegrity relatives are interesting, I do not believe that these structures qualify as tensegrities. With the deresonated structures, once the gap between two head-to-head struts gets closed and they get nailed to a strut slightly inside of them, the structural stability stems from the continuity of the struts between triangles. It is true that in most realizations where the strut needs to be bent slightly to make connections, it is pulling up on the strut underneath. However I believe this pulling is not essential to the structure and if the strut were permanently bent to fit (by say heat treatment) before being put in place, the structure would still be as stable without the strut exerting an upward force on the inside strut it is attached to. I think it is important not to confuse the tensions and force needed to shoe-horn in an ill-fitting component with the essential tensions that are innate to tensegrity. I should also state that this is somewhat armchair speculation on my part. Though I have put together geodesic models and many tensegrities, I have not put together a deresonated structure with bent-to-fit components. That being said, I think this chapter makes an interesting transition between tensegrities and geodesics. Just because there is a connection between two concepts, doesn't make one a subset of the other. For example, even though you saw a caterpillar become a butterfly, you wouldn't be wise to go around calling a caterpillar a type of butterfly or vice versa."

The appendices of calculated data and calculator routines are not needed today.

## Kenner, Hugh

## Table of Contents

Of interest to tensegrity researchers is Kenner's book on geodesic math.

## Geodesic Math and How to use It

Printed in 1976 and reprinted since, Kenner's text was the first, and remains a cogent, overview of the mathematics of tensegrity and geodesic structures.

Kenner took the position that geodesics are a special case of tensegrity structure. He wrote in the preface, "Fuller's geodesic domes constitute a special case of a larger class of Fuller constructs called Tensegrities, and the way to an intuitive understanding of domes is to understand Tensegrity first." Following this approach, part one of the book is about tensegrity mathematics, divided into six chapters of (1) weight vs. tension, (2) spherical tensegrities, (3) complex spherical tensegrities, (4) tendon system minima, (5) geodesic subdivision and (6) rigid tenesegrities.

Appendices contain data lookup tables, and programming code for the HP-65 calculator.

## Errata Criticism of the Book

Burkhardt maintains a list of errata and criticism here: http://bobwb.tripod.com/synergetics/hugh/index.html. Its highlights are

## Links and References

Geodesic Math and how To use It, on Google Books: http://books.google.com/books?id=arwzU5ZjE1YC&printsec=frontcover&dq=hugh+kenner+geodesic+math&hl=en&ei=UfimTLmQCcKSswbTw5WZDA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCoQ6AEwAA#v=onepage&q&f=falseErrata, hosted by Robert Gray, http://bobwb.tripod.com/synergetics/hugh/index.html

## Links and References

Wikipedia on Hugh Kenner, http://en.wikipedia.org/wiki/Hugh_Kenner

Portal To MathematicsPeople: Burkhardt, Connelly, Kenner, Hart, Whiteley