Activities: Mathematical Connections with a Spirograph

Flores, Alfínio; Prichard, Mary Kim; Bezuk, Nadine; Moody, Mally

doi:10.5951/mt.85.2.0129

Cited by 5 publications

(3 citation statements)

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“…(a) A hypocycloid with R=10, r=8, (b) A hypocycloid of R=30, r=24. In addition, another thing can be discovered that if the ring has m teeth, the hypocycloid formed with a gear of k teeth has the same shape as the hypocycloid formed with a gear of (m-k) teeth, which is the double generation theorem [13]. By investigating this property, it can be found that when the ring has m teeth, every epicycloid formed with gear of k teeth can be generated as a hypocycloid formed with gear of (m+k) teeth, which is not practical through physical sets.…”

Section: Number Of Teethmentioning

confidence: 99%

Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions

2023

TNS

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Perfectly symmetric curves always have a high degree of aesthetic value. While it is difficult to draw them by hand, Spirograph is an old and popular drawing toy that produces fascinating symmetric patterns. In playing with drawing software, the author explores types of Spirograph patterns, the type identification method, and the parametric equations to express Spirograph mathematically. This paper also discusses the key parameters of a Spirograph pattern and how they affect the pattern shape. Finally, Spirograph pattern design is carried out by analyzing the features of a random pattern and estimating its different parameters. These results to some extent demystify and predict the seemingly infinite Spirograph patterns, as the corresponding parameters of a given Spirograph pattern can be found so that the similar image can be drawn by hand through a physical Spirograph set.

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Section: Number Of Teethmentioning

confidence: 99%

Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions

2023

TNS

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“…[Cav75] uses basic axioms of mathematics to prove that the number of points to the figure generated is the greatest common divisor (GCD) of the number of teeth on the two gears. [Flo92] does likewise in using the Spirograph as a tool for explaining principles of arithmetic like LCM (Least common Multiple) and GCD. [She15] writes about the physical heritage of geometry in Germany when material models used to be made to demonstrate geometric principles.…”

Section: Spirograph Parametersmentioning

confidence: 99%

Flattening the Curve. . . of Spirographs

Konkar¹

2022

Recreational Mathematics Magazine

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The Spirograph is an old and popular toy that produces aesthetically pleasing and fascinating spiral figures. But are spirals all it can make? In playing with a software implementation of the toy, the author chanced upon a variety of shapes that it can make that are different from its well-known repertoire of spirals, in particular, shapes that have a visible flatness and not the curved spiral geometry that we are accustomed to seeing from the Spirograph. This paper reports on these explorations by the author and his delightful discovery of very elegant and simple geometric relationships between the Spirograph’s structural parameters that enable those patterns.

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“…Matematiksel ilişkilendirme, matematik ile bilgisayar, dil, fen, sanat, mimari, müzik, dans, tiyatro ve eğitim alanları gibi birçok disiplin arasında mevcuttur (Bodner, 2006). Matematiksel ilişkilendirmenin farklı disiplinler bağlamındaki somut örnekleri birçok araştırmanın konusu yapılmıştır (Bodner, 2006;Flores, 1992;Monroe & Mikovch, 1994). Bu doğrultuda matematiğin, müzik dersinde kesirlerle, görsel sanatlar da oran konusuyla, tarih dersinde zaman şeridiyle, fen dersinde ısı sıcaklık, sürat gibi konularla ilişkilendirilmesi öğrenme ve öğretme süreçlerinin niteliğini daha iyi hale getireceği söylenebilir.…”

Section: öğRetmen Adaylarının Matematiği Farklı Disiplinler İle İlişkilendirme Etkinlikleri Tasarlama Becerileriunclassified

The Skills of Prospective Teachers to Design Activities that Connect Mathematics to Different Disciplines

Özgen

2019

İnönü Üniversitesi Eğitim Fakültesi Dergisi

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The aim of this research was to examine the skills of prospective teachers to design mathematics connection activities with different disciplines. In the research it was asked that prospective teachers design a mathematical activity in which mathematics was connected with the ability to connect to different disciplines. For this purpose, the research was carried out using the case study model. The study group had 19 mathematics, 11 physics, and 10 chemistry prospective teachers. The designed activities were examined according to purpose, cognitive processes and mathematical competence and skills. As a result of the analysis of the obtained data, the concept of ratio-proportion was mostly mentioned in the designed mathematical learning activities. It was involved also in other mathematical concepts such as derivative, function, proposition and percentage. In the classification of the designed activities according to the aims, it was found that the consolidation activities were the most and the difficulties and the misconceptions activities were the least. The 5 groups of prospective teachers preferred to develop activities for new learning. When the activities designed by prospective teachers were classified according to the cognitive processes, they were designed to practice, evaluate, consider, apply and produce in descending order. The activities that were developed did not include interpret and create activities. According to mathematical competence and skills, problem solving, modeling and different representations activities were mostly involved. Activities for generalization, proof and reasoning and technology use were the least developed activities.

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Activities: Mathematical Connections with a Spirograph

Cited by 5 publications

References 0 publications

Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions

Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions

Flattening the Curve. . . of Spirographs

The Skills of Prospective Teachers to Design Activities that Connect Mathematics to Different Disciplines

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