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Record W3200939041 · doi:10.5206/mt.v1i1.14038

How to use Fibonacci numbers to teach recursive programming

2021· article· en· W3200939041 on OpenAlex
Jürgen Gerhard

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueMaple Transactions · 2021
Typearticle
Languageen
FieldComputer Science
TopicLogic, programming, and type systems
Canadian institutionsnot available
Fundersnot available
KeywordsFibonacci numberComputer scienceTheoretical computer scienceMapleMathematicsDiscrete mathematics

Abstract

fetched live from OpenAlex

There are too many examples and programming guides (which, e.g., an internet search for "recursive procedure Fibonacci" will turn up) to count that use Fibonacci numbers as an example to illustrate recursive programming. The motivation for this article is to show why the naive way of doing this is a bad idea, as it is horrendously inefficient. We will exhibit much more efficient ways of computing Fibonacci numbers, both iterative and recursive, and analyze and compare worst case running times and memory usages. Using some mathematical properties of Fibonacci numbers leads to the most efficient method for their computation. For illustration and benchmarking, we will use Maple and its programming language, however, similar behaviour can be demonstrated in almost any other programming language. This exposition combines and explores the mathematical properties of Fibonacci numbers, notions of algorithmic complexity, and efficient Maple programming and profiling techniques, and may be used as an introduction to any of these three subjects. The techniques described can be readily generalized to more general types of linear recurrences with constant coefficients.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.979
Threshold uncertainty score0.920

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0010.001
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.029
GPT teacher head0.255
Teacher spread0.226 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it