Direct, point-by-point inscription of fiber Bragg gratings by infrared femtosecond laser had been recently reported. Response of these gratings to annealing at temperatures in range 500C to 1050C is studied for the first time. Gratings inscribed by infrared femtosecond lasers were thermally stable at temperatures up to 900C, representing a significant improvement in comparison with the “common”...

Following the discovery of a series of geometric designs on the floor of the Biblioteca Laurenziana in Florence we analyse the “Medici panel”, which consists of a circular rosette containing a set of inscribed elliptical disks, with a view to regenerating the pattern. The geometry is shown to be surprisingly complex. We were able to determine a numerical solution for synthesising the pattern. A...

Imagine a sphere with its equator inscribed in an equilateral triangle. This Saturn-like figure will help us understand from where Cardano’s formula for finding the roots of a cubic polynomial p(z) comes. It will also help us find a new proof of Marden’s theorem, the surprising result that the roots of the derivative p(z) are the foci of the ellipse inscribed in and tangent to the midpoints of ...

An element of arc length or an element of surface area can naturally be approximated using either an inscribed object or a tangential object. An approach often followed is to use inscribed objects for arc length and tangential objects for surface area. Why the difference? This paper explores the roads less traveled. Both inscribed and tangential approximations can be used in either situation ar...

This is easily established, since according to the theorem of Euler mentioned above, if d denotes the distance between the centers of the circumscribed and inscribed circles, then d = R2rR. It follows that R~2rR^0, and therefore R^2r. Equality holds only if the two circles are concentric, that is, if the triangle is equilateral. The problem of generalizing the above result to space was proposed...

The r-Hofstadter triangle and the (1 − r)-Hofstadter triangle are proved perspective, and homogeneous trilinear coordinates are found for the perspector. More generally, given a triangle DEF inscribed in a reference triangle ABC, triangles A′B′C′ and A′′B′′C′′ derived in a certain manner from DEF are perspective to each other and to ABC. Trilinears for the three perspectors, denoted by P ∗, P1,...

Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality. This gives new ways to obtain rational (integer) right triangles from a given one. 1. Harmonic and Symphonic Squares Consider an arbitrary triangle with altitude α corresponding to base β (see Figure 1a). Assuming that the bas...

• Abstract Inscriptions on the body, especially tattoo, scarification, and body paint, have been part of ethnographic literature since before the birth of anthropology as a discipline. Anthropology's origins as the study of the exotic Other can be seen in the early descriptions of the body art of non-Westem peoples. Anthropologists have generally focused on how the inscribed body serves as a ma...

In this paper, a new design method considering a desired workspace and swing range of spherical joints of a DELTA robot is presented. The design is based on a new concept, which is the maximum inscribed workspace proposed in this paper. Firstly, the geometric description of the workspace for a DELTA robot is discussed, especially, the concept of the maximum inscribed workspace for the robot is ...

This case study considers an online market adoption as a process of technology transfer across contexts. This conception enables us to analyze the adoption difficulties from a technology inscription lens. This lens suggests that technology was developed based on a particular context which assumes how technology can be best used and how certain “practices” are inscribed. In this view, the adopti...