Matherialise

Crafting 3D sculptures involves a blend of math and a bit of tinkering... It’s sometimes an hectic process! Here's how I’m turning concepts into sculptures:

1. Tinkercad: Yeah, don’t laugh but… For very basic shapes, I’m using TinkercadJ Yes ! that very online and free tool for kids ! because, honestly, it is so easy and straightforward to use !
2. Surfer: A great tool that allows you to turn formulas into shapes Surfer is easy to use, fun, but you cannot export the forms it is just for display.
3. Mathmod: a wonderful application to generate objects from formulas, parametric, and an incredible objects library… Once you export objects from Mathmod, you need to add thickness to them with another tool (like blender) to print them
4. Blender: this free 3D software allows you to generate objects from python scripts, and/or to rework objects for printing (adding thickness, etc.) Blender
5. Printer: I’m using an Original Prusa i3 MK3S

To go further on tools and ideas, you can visit this fantastic site.

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Whilst diving into the world of mathematical sculptures, I was confronted to a wide range of shapes, each presenting specificities…
How to display them in a logic and understandable way ?
Here is my proposition of classification, from the simplest symmetry to the complexities of higher dimensions. There must be plenty of way to present categories, and I'm aware it can be improved, but, hey, I must start this journey with a map.

1. Pure Geometry and Symmetry

Starting with the basics, the "Pure Geometry and Symmetry" category is where simplicity meets elegance. Here, you will find geometric solids and symmetrical structures. Platonic or Archimedean solid, each object are inviting you to explore the fundamental principles of geometry.

2. Pavings and Tessellations

This is all about the mesmerizing world of Pavings and Tessellations, where art and mathematics weave together to form stunning patterns. From the historical complex mosaics that adorned ancient buildings to the non-periodic Penrose tiles, the danger here is to get stuck into a temporal loop while composing patterns !.

3. Topology and Surfaces

This section invites us to bend our minds and challenge our perceptions. Through sculptures like the Möbius strip and the Klein Bottle, we explore the world of continuous shapes, non-orientable surfaces, and knots… These objects allow us to grasp some concepts of topology, a branch of mathematics concerned with the properties of space that are preserved under continuous deformations. It's here that tactile experience is really helpful to experience and get it….

4. Fractals and Self-Similarity

In this category, we delve into the infinitely complex. Fractals, with their self-repeating patterns at every scale, offer a glimpse into the infinitely detailed. This sculptures here represent the chaos and order found in nature, from the branching of trees to the structure of snowflakes, all governed by simple mathematical rules that result in endless complexity.

5. Dynamics and Complex Systems

Coming soon…
This category will explore the unpredictable and often chaotic nature of dynamic systems... Through sculptures that represent strange attractors and Lissajous curves, we encounter the visual representation of systems governed by deterministic rules that can lead to complex and unpredictable patterns. It's a fascinating glimpse into the mathematical study of how systems evolve over time.

6. Computational Mathematics

Computational Mathematics merges algorithms with art, showcasing sculptures generated through computational processes. Here, Voronoi diagrams and Delaunay triangulations illustrate the power of computers to model and solve complex mathematical problems. Here, the only limits are imagination (and technical proficiency…)

7. Abstract Mathematics and High-Dimensional Concepts

Finally, this category aims to envision the unseeable : high-dimensional shapes and complex mathematical surfaces through 3D. Tesseracts and other hypercubes become almost graspable, providing a bridge to understanding the complexities of higher-dimensional spaces.

I hope this collection of mathematical sculptures will help you experience and understand the rich tapestry of mathematics that underpins our world, from the tangible and familiar to the abstract and profound. From my perspective, it’s really fun to bring it to you.

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In the realm of mathematics, abstract concepts are like a distant mystery, far from our tangible reality.
As a math enthousiast –and modest beginner- I wanted to try to bridge this gap, by bringing to the real life beautiful mathematic sculptures.
I wanted to turn the invisible world of mathematics into something you can hold in your hand.
This site aims at giving a hint for anyone who's fascinated by the intersection of math, art, and technology. It will be progressively filled with a set of mathematical sculptures, from simple geometric shapes to complex topological forms. This site also intents to give the opportunity to get a grasp to those hard-to-wrap-your-head-around concepts, which is, dare I say, pretty exciting 
As any math enthousiast will say, there is not only an inner beauty into math. These sculptures tie into physics as well as decorative arts, with their patterns and symmetries that mirror the laws of the universe, and architecture, offering inspiration for sleek and sustainable designs.
So I just wanted to share up a view of mathematical art to any person interested, whether you're a student, a teacher, or just someone who loves to think or tinker: you can download and 3D print these sculptures. It turns maths into a hands-on experience, shining a light on the subtile link between math and artistry behind it.
I’m just starting this site so don’t hesitate to give me a shout, to suggest any improvement, but please be indulgent, I’m doing it just for my pleasure and for learning because as Richard Feynman once said: « What I cannot create, I do not understand », I like to understand concepts in detail to make them my own.
Ready to jump in and see where math and art blend? Let's explore this together!

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