Golden Ratio and Fibonacci's Sequence

thingiverse

The Golden Rectangle Project: Building Blocks for Math Success This innovative project aims to bring the Golden Ratio concept to life, enabling students to grasp its underlying mathematics in a fun, interactive way. **Printer Settings** Printer Brand: RepRap Printer Model: prusa i3 Rafts: Doesn't Matter Supports: Doesn't Matter Resolution: 0.2mm Infill: 10% **Printing with Impact** Using white plastic, students can personalize each block by painting it their preferred color, creating a visually engaging representation of mathematical concepts. **Design Process** Each component was carefully crafted using simple sketches in 123D Design. Starting with a square measuring 1 cm on each side, the design evolved into an arc inscribed within the square. Two different heights (2mm for the square and 10mm for the bow) were then extruded to create the foundation of 1cm x 1cm x 1cm. As we build upon this base, we follow the Fibonacci sequence: 1, 1, 2, 3, 5, 8. By scaling the sides while keeping the height constant, students develop a deeper understanding of mathematical proportion and relationships. The finished project takes on a stunning bas-relief design, where each module's length is intricately etched into the geometry of the Golden Section or Fibonacci sequence. **Project Overview: Math Comes Alive** The Golden Rectangle project lets students engage with the Golden Ratio and Fibonacci sequence in a hands-on way. By printing and assembling the components, they'll gain a comprehensive grasp of these fundamental mathematical concepts. **Steps to Build the Golden Rectangle** 1. **Draw the Sketch**: Create a 10mm square using the rectangle tool from the sketch menu. 2. **Extrude Shapes**: Extrude the shapes with two different heights (2mm for the square and 10mm for the bow), resulting in a foundation measuring 1cm x 1cm x 1cm. 3. **Add Fillet**: Enhance the design by adding a fillet to create rounded corners. 4. **Duplicate and Scale Blocks**: Create multiple blocks following the Fibonacci sequence: * Duplicate the first block, rotating it 90 degrees counterclockwise. * Scale the first block to 20mm x 20mm, then rotate 90 degrees clockwise. * Repeat this process for each block (10mm, 20mm, 30mm, 50mm, and 80mm). 5. **Optional Step**: Add text to each block, displaying its corresponding value using the sketch feature. **Results** By working through this project, students will develop a tangible understanding of abstract mathematical concepts, such as the Golden Ratio and Fibonacci sequence. The three-dimensional representation serves as a lasting memory aid for these essential principles.