Discovers and analyzes the proportions of the Golden Section in the rare stone tablet, Tablet of Sippar, representing the four main feats of the god Marduk. (ASK)

Introduces data collated by Glendon Lean on nearly 900 counting systems in Papua New Guinea, Oceania, and Irian Jaya (West Papua) which came from a questionnaire completed by students and talks with village elders. Lean's thesis on the spontaneous developments of these ancient cultures challenged traditional theories describing the spread of…

For the last several years teachers have been using counters and connected cube "trains" and creating base-10 block models to help students develop number sense and understand number concepts. It is described how ten-frame tiles could be more useful tool for building number understanding for many students.

This study compares the tendency for numerals to elicit spontaneous perceptions of colour or taste (synaesthesia) with the tendency to visualise numbers as occupying particular visuo-spatial configurations (number forms). The prevalence of number forms was found to be significantly higher in synaesthetes experiencing colour compared both to…

This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…

Computational precision is sometimes given short shrift in a first programming course. Treating this topic requires discussing integer and floating-point number representations and inaccuracies that may result from their use. An example of a moderately simple programming problem from elementary statistics was examined. It forced students to…

A teacher shares his successful experience in helping students understand the relationship between exponents and logarithms in high school and college courses. He presents the procedure that he used for teaching using a graphing calculator that shows previous calculations made.

Linguistic descriptions of sign languages are important to the recognition of their linguistic status. These languages are an essential part of the cultural heritage of the communities that create and use them and vital in the education of deaf children. They are also the reference point in language acquisition studies. Ours is exploratory…

Within the set of points in the plane with integer coordinates, one point is said to be visible from another if no other point in the set lies between them. This study of visibility draws in topics from a wide variety of mathematical areas, including geometry, number theory, probability, and combinatorics.

We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

Advocates of the ''continuity hypothesis'' have argued that innate non-verbal counting principles guide the acquisition of the verbal count list (Gelman & Gallistel, 1978). Some studies have supported this hypothesis, but others have suggested that the counting principles must be constructed anew by each child. Defenders of the continuity…

To account for the mechanism of number transcoding, many authors have proposed various models, for example, semantic-abstract model, lexical-semantic model, triple-code model, and so on. However, almost all of them are based on the symptoms of patients with left cerebral damage. Previously, I reported two Japanese patients with right posterior…

Two experiments were conducted to test the hypothesis that toddlers have access to an analog-magnitude number representation that supports numerical reasoning about relatively large numbers. Three-year-olds were presented with subtraction problems in which initial set size and proportions subtracted were systematically varied. Two sets of cookies…