The heliocentric path of the Moon

In his Astronomie populaire, Camille Flammarion points out that the heliocentric path of the Moon, which, according to him, has generally been represented as a sinuous curve, is actually concave everywhere towards the Sun. Flammarion’s observation is the starting point of this study which goes backwards in time, via often misinformed authors, to the mathematician who first established this counterintuitive property by means of a purely geometrical proof. The story also includes a heated debate between readers of a British periodical. Beginning in France at the end of the 19th century, the journey finishes in Scotland in the first half of the previous century.

The reality of employing the mathematics lab and its relationship to developing geometrical proof skills among high school students

The study aimed to reveal the reality of employing the mathematics laboratory and its relation to the development of geometrical proof skills among high school students. Descriptive and semi-experimental methods were used to answer the research questions, and the study conducted a questionnaire administered to the secondary school teachers aimed at revealing the reality of employing the mathematics laboratory from their point of view and a list of geometrical proof skills necessary for high school students. A random sample was selected and represented by the research community that includes female teachers and female students in the secondary stage in Jubail city. The research sample consisted of (12 teachers and 58 students) divided into two groups, the first group included 28 students who studied geometrical proof by employing the mathematics laboratory, and the second group included 29 students who studied geometrical proof without employing the mathematics lab. The results showed that the reality of employing the mathematics laboratory from the point of view of the secondary school teachers in Jubail city was generally moderate, as there are statistically significant differences at the level of (0.01) of the means of scores between the first group and the second group in the skill of inferring relationships and the skill of the evaluation of proof due to the employment of the mathematics laboratory.

A Proof of Komlós Theorem for Super-Reflexive Valued Random Variables

We give a geometrical proof of Komlós’ theorem for sequences of random variables with values in super-reflexive Banach space. Our approach is inspired by the elementary proof given by Guessous in 1996 for the Hilbert case and uses some geometric properties of smooth spaces.

Metaphysics and the Mathematical Diagram

Accounts of geometry are caught between the demands of history and philosophy, and are difficult to reduce to either. In a profoundly influential move, Plato used geometrical proof as one means of bootstrapping his Theory of Forms and what came to be called metaphysics, and the emergence of ontological modes of thinking. This has led to a style of thinking still common today that gets called ‘mathematical Platonism’. By contrast, the sheer diversity of mathematical practices across cultures and time has been adduced to claim their historical contingency, which has recently prompted Ian Hacking to question why there is philosophy of mathematics at all. The different roles assigned to geometrical diagrams in these debates form the focus of this chapter, which analyses in detail the contrasting discussions of diagrams, and of the linearization and spatialization of thinking, by Plato (especially Meno and the Republic), by the cognitive historian Reviel Netz, the media theorist Sybille Krämer, and the anthropologist Tim Ingold.

Facts indicate that Fermat had a simpler proof for his last theorem!

1.Fermat really had a simple proof for his last theorem. This is because, at that time, the knowledge of “elliptical curves” used for present proof was not there. So, he never had proof in its present form. The present proof is so complicated to write even in a book having a big margin!2.He never had the wrong proof.His ability of solving his previous tricky puzzles and theorems proves that he used to check very proof perfectly before telling it to his friends. In fact, he proved the above theorem for a particular case of n=4.3.His comment of “the margin of this book is insufficient to write the proof” indicates to me that it must be a geometrical proof, using some triangles.