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Thursday 10 March 2016

Fibonacci spiral

The Fibonacci spiral is based on the Fibonacci sequence to construct a curve forming a spiral. This spiral and some variants appear in the constructions of live entities. In this article we present a computed, interactive version of this spiral with the help of Dr. Geo, an interactive geometry and programming application. Later we discuss on the interest of this approach in mathematics secondary teaching.

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Tuesday 23 February 2016

La spirale de Fibonacci

La spirale de Fibonacci s'appuie sur la suite éponyme pour la construction d'une courbe en forme de spirale, cette spirale et ses variantes apparaissent dans des constructions du vivant. Dans cet article nous proposons une construction calculée d'une forme interactive de cette courbe, à l'aide de Dr. Geo, logiciel de géométrie interactive et de programmation. Nous relaterons ensuite les liens à faire avec les programmes d'enseignement secondaire de mathématiques.

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Wednesday 10 February 2016

Drawing the Parabolic Trajectory of an Object under Gravity

Parabolic trajectory under gravity [Thanks to Hilaire for editing and typesetting the article in TeXmacs and provided the pdf version much more pleasant for reading and printing. Traduction française: Construire la trajectoire parabolique d'un objet soumis à la gravité.]

When you throw an object into the air, its trajectory is a parabola. How do its instantaneous velocity and the vertical and horizontal components of the instantaneous velocity change over the course of its trajectory? What happens when the initial speed is larger? Smaller? What happens if the gravity were larger? Smaller? Zero? Negative? Holding gravity and the initial speed constant, in which direction can you throw to make the object reach the farthest point along the horizon? This sketch created using Dr. Geo can help a high school physics teacher explore all these questions with her/his students.

In this article we will show you how to construct this gravity sketch. The reader is assumed to be familiar with the basics of Dr. Geo such as drawing parallel lines and changing the colors/names/styles/... of the points and lines. Note: To avoid a bug, you need to update your Dr. Geo to 16.03 or later. Also, you may want to "save session" so as to make the upgrade permanent.

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Saturday 17 October 2015

Programmation recursive

Aborder la récursivité n'est pas aisé pour les néophytes. Voici une approche pas à pas de la construction du triangle de Sierpinski pour appréhender sa dimension auto-répétée.


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Termes d'une suite

On continue avec les suites ou comment afficher les termes d'une suite qui est chaotique pour certaines valeurs de son paramètre.

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Diagramme de suite récurrente

Vous avez sans doute tous ce souvenir de classe de terminale, des suites récurrentes, avec recherche d'un point fixe d'une fonction. Dr. Geo permet d'explorer ce sujet.

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Saturday 21 February 2015

Form validation and WebWidget

Remember my previous post? I conclude with the question: How to get back my form validation with my new WebAddress widget? Let's see how to get it back.

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Friday 20 February 2015

WebWidget in question

An aspect I was curious about AidaWeb application server: how do you build reusable component? I know a bit about Seaside, but I had no clue how to achieve it with Aida. It turns out to be very easy.

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Thursday 19 February 2015

Ajax for the dummies

As a Smalltalk developer, I have a strong opinion when it comes to programming language. This turns to a tendency to write application with only Smalltalk code. When it comes to state-of-the-art in web application development, this habit is really a problem, and I turn myself as a complete dummy to the HTML5 interlaced technologies, particularly Ajax and Javascript. Although the benefits of such technology is perfectly understandable, it appears to me as plates of spaghetti. This is where Aida shows up and is my hero du jour.

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Wednesday 18 February 2015

Aida and input field validation

For a new project, I have been looking for a Smalltalk web server to design a web application. I have been previously exploring Seaside+Magritte and more recently - a couple of hours ago - I took a fresh look at Aida. And to say the true, I have been impressed by how it can be simple and yet effective to handle my problem. Let's take a look at its field validation approach.

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Friday 22 August 2014

Les trois portes

Un problème classique de probabilité modélisé avec une figure Smalltalk.

« Un vizir montre trois portes, A, B et C à Sinbad, son mathématicien. Il lui explique que derrière l’une d’elles se trouve une pièce d’or et que rien ne se trouve derrière les deux autres. Si Sinbad choisit la bonne porte, il gagne la pièce d’or.

Sinbad choisit une porte sans l’ouvrir.

A ce moment-là, le vizir lui explique : « Je vais maintenant ouvrir une des deux portes que vous n’avez pas choisie et derrière laquelle il n’y a rien. »

Le vizir, comme promis, ouvre une porte et dévoile un espace vide. Il ajoute : « Je vous offre donc la possibilité de changer votre choix ou pas. Que faites-vous ? »

Sinbad sourit, car il connaît « LA » stratégie pour gagner le plus souvent possible.

Détermine cette stratégie.

Notons bien qu’à chaque partie les choses se déroulent de la même façon : Sinbad a la possibilité de changer son premier choix après avoir vu la porte ne donnant rien. Le vizir sait où se trouve la pièce d’or. »

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Wednesday 14 August 2013

Animated Smalltalk sketch

An example coming from the Dr. Geo user guide:

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Thursday 15 December 2011

Dr. Geo: hacker spirit in a candy box

When you teach mathematics at secondary schools, you enjoy using interactive geometry software with your students. Dr.Geo is one such free software, it comes with some unique features. With such software, students learn geometry the way it should be learned -- by drawing, but Dr. Geo goes one step further.

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Saturday 12 February 2011

Dr. Geo and block closure

Dr. Geo comes with a few power tools related to programming. Since its first incarnation, Dr. Geo is enriched with open doors to let the user explores new way to use Dr. Geo. The first version of Dr. Geo was developed in C++, with that version the power tools came under the form of a Scheme interpretor embedded in Dr. Geo. This Scheme was GNU Guile and it gave freedom to write script or programmed sktech with the scheme language.

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Thursday 20 January 2011

Paradigm shift

With recent releases, and coming version 11.03, Dr. Geo II is becoming more and more an integrated environment to teach or to learn interactively software programming within a geometry and math context.

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Thursday 8 July 2010

Sierpinski triangle

How to construct with Smalltalk script the Sierpinski triangle.

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Saturday 10 January 2009

Les scripts avec Dr. Geo II

Dans cet article je montrerai comment utiliser les scripts Dr. Geo II pour construire dans une figure la courbe représentative d'une fonction, puis la tangente en tout point de cette courbe. La logique de construction de la figure sera indépendante de la fonction. courbeTangente3.png

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