Logic, geometry and visualisation of the body in Acquapendente’s rediscovered Methodus anatomica (1579)

The article provides the first description and analysis of the recently rediscovered manuscript titled Methodus anatomica by Girolamo Fabrici da Acquapendente (1533–1619). Acquapendente was one of the most important anatomists in late sixteenth-century Europe and played an instrumental role as Harvey’s teacher in Padua towards the latter’s discovery of the circulation of the blood. The manuscript provides first-hand testimony as to how anatomy was administered in Padua in the post-Vesalian era and sheds light on a number of otherwise unknown aspects of the development of the anatomical method. Chiefly among these is the attention devoted by Acquapendente to historia, as a way to order sensory data in a consistent way, which draws widely from the geometrical method and from the contemporary debate on the discretisation of continuous quantities.

Trajectory planning and optimization of the bionic mantis robot front leg

In this paper, a manipulator of the bionic mantis robot is designed inspired by the anatomical structure of the mantis front leg. A geometrical method is utilized to calculate the forward kinemics. Then, by analyzing the mantis motion video frame by frame, each of the front leg joints angles is measured in crawling and preying motion, which are used as interpolation conditions to solve the planned trajectory for manipulator by cubic spline interpolation. In some circumstance, the planned joint angles may exceed its limitation. By undermining the interpolation conditions, the problem is transformed from solving a cubic spline function to optimization. Finally, particle swarm optimization with variable inertia weight is introduced to optimize the planned trajectory. The result indicates that the trajectory, smoother after optimization could effectively imitate the motion of mantis front leg within the joint rotation range, which lays the basis for further research on the motion control.

A new geometrical method for portfolio optimization

Risk aversion plays a significant and central role in investors’ decisions in the process of developing a portfolio. In this portfolio optimization framework, we determine the portfolio that possesses the minimal risk by using a new geometrical method. For this purpose, we elaborate an algorithm that enables us to compute any Euclidean distance to a standard simplex. With this new approach, we can treat the case of portfolio optimization without short-selling in its entirety, and we also recover in geometrical terms the well-known results on portfolio optimization with allowed short-selling. Then, we apply our results to determine which convex combination of the CAC 40 stocks possesses the lowest risk. Thus, we not only obtain a very low risk compared to the index, but we also get a rate of return that is almost three times better than the one of the index.

K1986BE92QI and STM32F103C8 microcontrollers as signal processing devices: comparative analysis

The subject of the research is to compare domestic microcontroller versus foreign microcontroller while used as signal processing devices in general applications. The purpose of the research was to conduct a comparative analysis of the popular foreign microcontroller STM32F103C8T6 and its domestic analogue K1986BE92QI in plastic package through solving a typical problem in the form of a 64-point FFT computation and calculating the value of π number by the geometrical method. The obtained results are in line with those expected in terms of program execution time and stability of the debug mode in the MDKARM v5 development environment. In the course of research, the key features of working with the examined microcontrollers were identified. Practical relevance of the research consists in its practical applicability: the findings can be used as a supportive material in the creation of programmable radio engineering systems based on the microcontrollers under consideration.

Jak pokazać to, czego pokazać nie można? O obrazowaniu liczb niewymiernych

In this article, I would like to draw attention to the cognitive potential of an image, showing how significant the role of visual imagination in mathematics is. I will focus here mainly on the possibilities of visualizing irrational numbers.Our starting point is the intuitive case of the square root of two, observed in the diagonal of a square. We will also discuss a simple, geometrical method of constructing the square roots of all integers. Next, we move over to the golden ratio, hidden in a regular pentagon. We will use a looped, endless animation to visualize the irrational number φ. Then we will have a closer look at the famous number π and discuss two different attempts to find its visual representation. In the last two sections of the article, we consider the possibility of indicating rational and irrational real numbers and also grasp the whole set of real numbers.All the issues discussed in this article have inspired visual artists to create artworks that can help to understand relatively advanced mathematical problems.