Analysis of hyperboloid cooling tower projection on 2D shape

This paper undertakes the problem of mapping a hyperboloid cooling tower on a single plane. Measurements performed by ground-based laser scanning technology quickly deliver substantial amounts of geometric data of the tower’s outer wall. The essence of the article is projection of the rotational hyperboloid on a plane. The shape of the hyperboloid cooling tower is not directly expandable to a single plane. Mapping a hyperboloid shape on a plane is, therefore, associated with distortions. This paper presents a comparison between cylindrical and conic projection of a hyperboloid cooling tower. The most popular method of mapping hyperboloid is cylindrical projection. The cylinder’s side surface is easily developed on the drawing sheet. For the hyperboloid cooling tower, the biggest distortions occur in the latitudinal direction and reach the highest values at the top and bottom edges. The equation (13) describe distortion for the cylindrical projection. The equation (18) describe distortion for the conical projection. This paper presents results obtained from the performed measurement. The analysis found that cone mapping produces less distortion than cylindrical projection for the hyperboloid cooling tower. We think, that in conical projection, the shape of a hyperboloid cooling tower and theoretical conic shape have better corresponding together than in cylindrical projection.

Cutaneous horn arising from the scrotum

A cutaneous horn, cornu cutaneum, is a hard, conical projection composed of compacted keratin that resembles the horns of animals. They commonly occur on sun-exposed areas, including the head, ears, forearms and hands. Cutaneous horns are extremely rare. Although most are benign in nature, a significant portion may harbour a malignant or pre-malignant lesion, and histopathological analysis of the base of the lesion is imperative to categorise it as one of benign aetiology or one of a more sinister pathology. We present a case of a 46-year-old male who presented with a 2-month history of a painless, firm, rapidly growing conical projection arising from his scrotum. Clinically, a non-tender curved, yellow-brown, horn-like projection was observed arising from the median raphe of his scrotum. With informed consent, a full-thickness excision, with adequate excision of the base of the horn, was performed under local anaesthesia. Macroscopically, the exophytic keratinous lesion was 7.5 cm long and 1.8 cm wide, with the length of the horn far outweighing the width at its base. Histopathological analysis confirmed the presence of a cutaneous horn arising from a condyloma acuminatum as evidenced by a verruciform architecture with tiers of parakeratosis in association with hypergranulosis and koilocytes. No dysplastic or malignant changes were present in the epithelium. According to our knowledge, this is the first case in the English literature of a cutaneous horn arising from the scrotal skin.

Cartographic conic projections and their appliance in national cartography

This paper is dedicated to the mapping of conic projections and their appliance in producing maps of our state cartography. So far they were often applied, and will be used precisely coned, polyconed and modified polyconed projections for the official mapping (1:500 000, 1:750 000, 1:1000 000 and 1:1500 000). In particular, they cartographic conical projection at a scale of 1:1000 000 were taken into consideration. Those are the Lambert conformal conical projection with two standard parallels and the Modified polyconic projections. In addition to these cartographic conical projections, is described Boneo`s pseudoconic equivalent projections. This is one of the cartographic conical map projection that is commonly used in the preparation of thematic maps as well as for atlas editions of geographic maps both in Serbia and abroad.

LA GÉOMÉTRIE DE L'ASTROLABE AU Xe SIÈCLE Geometry of the Astrolabe in the Tenth Century

Many studies on the astrolabe were written during the period from the ninth to the eleventh century, but very few of them related to projection, i.e., to the geometrical transformation underlying the design of the instrument. Among those that did, the treatise entitled The Art of the Astrolabe, written in the tenth century by Abū Sahl al-Qūhī, represents a particulary important phase in the history of geometry. This work recently appeared in a critical edition with translation and commentary by Roshdi Rashed. It contains the earliest known theory of the projection of the sphere, a theory developed in a commentary written by a contemporary mathematician, Ibn Sahl. Following R. Rashed, the present article offers here a thorough mathematical analysis of al-Qūhī's treatise and of the commentary by Ibn Sahl. It also presents, with commentary, an account of a contemporary treatise on the projection of the sphere, written by al-[Sdotu]āġānī. The latter work is concerned with the conical projection of a sphere on a plane, from a point on an axis of the sphere, other than its pole. The author consciously avoids the case of stereographic projection, but he studies all the other cases of conical projection which, if we employ the terms of al-Qūhī's theory, are compatible with the movement of the instrument (i.e. the rotation of the sphere around its axis). These three texts provide clear evidence of the emergence, during the second half of the tenth century, of a new field of study, that of projective geometry.

Coccidian parasites (Apicomplexa: Eimeriidae) of Chelydra serpentina (Testudines: Chelydridae) from Arkansas and Texas, U.S.A., with descriptions of Isospora chelydrae sp. nov. and Eimeria serpentina sp. nov.

Two new species of Coccidia (Apicocomplexa: Eimeriidae) are described from the feces of common snapping turtles, Chelydra serpentina serpentina, from Arkansas and Texas, U.S.A. Oocysts of Isospora chelydrae sp.nov. were found in 3/9 (33%) turtles and are symmetrical, 9.6 × 6.8 (9–11 × 6–8) μm, and bear one conical projection on one side of the oocyst and two conical projections on the opposite side of the oocyst, 1.5 – 1.6 μm long; shape index 1.4 (1.2 – 1.6). A micropyle, oocyst residuum, and polar granule are absent. Sporocysts are ellipsoid, 5.8 × 4.0 (5 – 7 × 3.8 – 4.2) μm, with a small Stieda body but no substieda body; shape index 1.5 (1.3 – 1.7). Oocysts of Eimeria serpentina sp.nov. were found in 4/9 (44%) of the turtles and are ellipsoid, 12.8 × 8.1 (11 – 15 × 7 – 10) μm; shape index 1.6 (1.4 – 1.9). A micropyle, oocyst residuum, and polar granule are absent. Sporocysts are ellipsoid, 7.6 × 4.1 (6 – 9 × 4 – 5) μm, each with a Stieda body but a substieda body is absent; shape index 1.8 (1.5 – 2.1). In addition, E. chelydrae Ernst, Stewart, Sampson, and Fincher, 1969 and E. filamentifera Wacha and Christiansen, 1979 were found in 4/9 (44%) and 1/9(11%) hosts, respectively.