Washington Military Department

SummaryBiangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the 19th century. Contemporary students will enjoy plotting biangular relations and discovering patterns in families of relations. The mathematical shapes which are given by biangular relations include standard shapes like lines, circles, hyperbolae and also unusual curves like.

The Planet on the Screen:Scales of Belonging in A. R. Ammons's Sphere Susannah L. Hollister (bio) A. R. Ammons ends his book-length poem Sphere: The Form of a Motion (1974) where his idea for it began—with the image of the earth seen from space. More than twenty years after writing the poem, he recalled the effect of the image's appearance: Sphere had the image of the whole earth, then for the first time seen on television, at its center…. There was the orb. And it seemed to me the perfect image to put at the center of a reconciliation of One-Many forces. While I had had sort of philosophical formulations for the One-Many problem before, the earth seemed to be the actual body around which these forces could best be represented. So when I began Sphere, I knew what I wanted to do. I wanted to kind of complete that process, that marriage of the One-Many problem with the material earth. (Set in Motion 103) The Apollo space program gave Ammons the metaphor he had long sought: a vehicle that combined the variety of the physical world into a single, unified object. The image had been put to a variety of uses—from commercial advertising to environmental advocacy—already, and Ammons saw its relevance to his own, poetic concern, "the One-Many problem."1 This contradiction had guided his [End Page 662] thought from his earliest writings; nearly every poem in his Collected Poems, 1951–1971, which he prepared just prior to writing Sphere, tries a perspective on the relation of unity and multiplicity. The contrast that concerns him results, fundamentally, from shifts in the scope of one's attention. What appears unified at one scale (the human body, for example) becomes partial (a single member of a society or a species) when one's view widens, and divisible (a group of cells) when one's view narrows. Ammons makes a poetics out of this constant possibility of reframing and uses it to generate a sense of social belonging at the same time that he holds to his experience of separateness. Shifts in attitude mark his very process of composing Sphere; he cut and revised the poem substantially from a first draft. Tracing his changes to the poem (in particular, his changing use of the image of the earth), the friendship that guided those changes, and Ammons's stated reactions to his own work reveals his tendency to alter a perspective as soon as he takes it. For Ammons, these shifts take part in the ongoing act of relating to readers and others with whom he identifies from a distance that often precludes any interaction at all. The phenomenon of space exploration reminds Ammons that the earth includes him and all he sees in its constant orbits and rotations. The short poem "Spaceship" shows him marveling at the difference between what happens at the scale of the cosmos and what happens at the scale of his house: It's amazing allthis motion goingon andwater can lie stillin glasses and the gascan in thegarage doesn't rattle. (Collected Poems 322) [End Page 663] The word can, both noun and verb here, locates the potential that impresses Ammons, the potential for stillness, in plain, household objects. Thinking of the activity that continues beyond observation transforms activity's absence—which appears in the poem's more inert lines, "on and" and "can in the"—into an "amazing" event. The Apollo 8 broadcast introduced the same contrast by showing, for the first time, the planetary scale in the same physical reality as more familiar, human scenes. The image of the earth it presented was more than a metaphor to Ammons; he considered it the "actual," "material" body in which the one-many problem inheres, as he said in the interview quoted above, and the perceived truth of the image was the source of its effect. The idea of the planetary image had become more strongly present in the public consciousness with the development of satellite technology in the 1950s; U.S. viewers had anticipated the photographs for years before Apollo...

Howard C. Rice, Jr., and Anne S. K. Brown, translated and edited by. The American Campaigns of Rochambeau's Army, 1780, 1781, 1782, 1783 Volume I, The Journals of Clermont-Creuecoeur, Verger, and Berthier; volume 2, The Itineraries; Maps and Views. Princeton: Princeton University Press; Providence: Brown University Press. 1972. Pp. xxviii, 351; v, 204, 177 plates, 345-62. $100.00 the set and Catesby Willis Stewart. The Life of Brigadier General William Woodford of the American Revolution. In two volumes. Richmond, Va.: Whittet and Shepperson. 1973. Pp. xiii, 743; 745–1446. $30.00 the set Get access Rice Howard C.Jr., and Brown Anne S. K., translated and edited by. The American Campaigns of Rochambeau's Army, 1780, 1781, 1782, 1783. Volume 1, The Journals of Clermont-Crèvecoeur, Verger, and Berthier; volume 2, The Itineraries; Maps and Views. Princeton: Princeton University Press; Providence: Brown University Press. 1972. Pp. xxviii, 351; v, 204, 177 plates, 345–62. $100.00 the set. Stewart Catesby Willis. The Life of Brigadier General William Woodford of the American Revolution. In two volumes. Richmond, Va.: Whittet and Shepperson. 1973. Pp. xiii, 743; 745–1446. $30.00 the set. Robert W. Coakley Robert W. Coakley Center of Military HistoryWashington, D. C. Search for other works by this author on: Oxford Academic Google Scholar The American Historical Review, Volume 79, Issue 4, October 1974, Pages 1254–1255, https://doi.org/10.1086/ahr/79.4.1254 Published: 01 October 1974