Origami, the art of paper folding, is not just a visually stunning craft but also an engaging tool to explore mathematical concepts. In this blog post, we’ll delve into how origami can be a gateway to understanding fractions and ratios, starting from basic folds to more intricate designs.
Origami can provide a practical and visual way to explore fractions and ratios. For instance, folding a paper into halves, quarters, or other fractional parts can help demonstrate these concepts in a tangible way. Additionally, ratios can be illustrated through the proportions of folds and the resulting shapes in origami creations. This hands-on approach can make abstract mathematical ideas more accessible and engaging for learners.
Basic Folds and Fractions
Halves and Quarters: Folding a square paper in half horizontally and vertically demonstrates halves and quarters. Each fold represents a division of the paper, providing a visual representation of fractions.
Eighths and Sixteenths: Further folding can lead to eighths and sixteenths. For example, folding the quarters in half will give you eighths, and folding those eighths in half will result in sixteenths.
Ratio Exploration
Aspect Ratios: When working with rectangular paper, folding it can alter its aspect ratio. For instance, folding a rectangle in half can change its dimensions, illustrating the concept of ratios between the length and width.
Proportional Folds: Origami designs often involve proportional folds, where specific ratios determine the placement of folds. For instance, folding a paper at 1/3 or 2/5 of its length creates proportional segments. Understanding and manipulating these ratios contribute to creating accurate and aesthetically pleasing origami models.
Fractional Origami Models
Modular Origami: Many modular origami models involve creating multiple units and assembling them. Understanding fractions is crucial for determining how many units are needed to complete the entire model.
Fractional Parts in Designs: Some origami designs incorporate fractional parts explicitly. For instance, a design might instruct you to fold a specific fraction of a section to achieve a certain detail or symmetry.
Advanced Concepts
Golden Ratio: Exploring more advanced origami designs may involve the golden ratio. Some designers use this mathematical concept to create aesthetically pleasing proportions in their models.
Fractional Angles: Certain folds may involve creating angles that correspond to specific fractional parts of a full circle. This introduces trigonometric concepts in the context of folding.
In conclusion, origami isn’t merely an artistic endeavour but a hands-on mathematical journey. From the simplicity of halves and quarters to the elegance of the golden ratio, origami provides a tangible and creative approach to exploring fractions and ratios, making mathematical concepts come to life in folded paper.
