Les fractales: une nouvelle source d'inspiration pédagogique, musicale et scientifique
Bibliographic record
Abstract
Math teachers often make use of graphs to visually represent equations and concepts based on the expected curriculum. Thus, I decided to investigate the possibility of converting an equation, normally interpreted using a graph, into auditory form, by converting geometric shapes into sound. To do so, I decided to use the celebrated Mandelbrot fractal, which uses the general equation z = z2 + c as a basic geometric concept. I then converted each equation, derived from a complex number, into a series of frequencies or audible musical notes. Each series was played on a computer and represented in graph form, so that the mathematical self-similarity could be observed. The results obtained show that one can hear this self-similarity, and suggest that it would be possible to use auditory methods in conjunction with traditional pedagogical methods to teach mathematics. Lorsqu’on étudie les mathématiques, nos enseignants font appel à l’utilisation de graphiques afin de représenter les équations et concepts que nous devons apprendre. C’est dans cette optique de pensée que j’ai entrepris l’investigation la possibilité de convertir une équation, normalement interprétée graphiquement, et de l’interpréter de manière auditive, c’est-à-dire, de transformer la forme géométrique en forme sonore. Pour ce faire, j’ai décidé d’utiliser, comme forme géométrique de base, la célèbre fractale de Mandelbrot, dont l’équation itérative est z = z2 + c. Par la suite, j’ai converti chaque itération provenant d’un nombre complexe quelconque en une série de fréquences ou notes de musique pouvant être perçues par l’oreille humaine. Cette série est alors jouée à l’ordinateur et représentée graphiquement afin d’en observer l’autosimilarité. Les résultats obtenus démontrent que l’on puisse entendre cette autosimilarité et suggèrent qu’il serait possible d’utiliser l’audio comme moyen pédagogique complémentaire dans l’apprentissage des mathématiques.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.006 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".