Fun with Figures

Geometry and astronomy may seem like two distant disciplines, but in reality, they share a deep and ancient connection. Since ancient times, humans have looked to the stars and traced imaginary lines between them to create constellations (figures that often form geometric shapes such as triangles, trapezoids, and lines of symmetry). This connection between geometry and astronomy is a fascinating opportunity to work on spatial, mathematical and cultural concepts in the classroom. When observing constellations, it is easy to identify simple geometric shapes: triangles, straight lines, trapezoids or more complex figures constructed by joining points (stars) in the sky. For example, the constellation Orion can be seen as forming a rhombus with a belt of three stars in the center. The Big Dipper, part of Ursa Major, resembles a trapezoid with a curved handle, and other constellations like Cassiopeia take the form of a zigzag that introduces students to concepts of angles and symmetry. Figur...

Origami, also known as origami, is much more than an artistic activity or a relaxing pastime: it is an extraordinary tool for exploring geometry in a tangible, creative and meaningful way. Each fold we make in a sheet of paper invites us to think about lines, angles, symmetries and proportions.  Folding paper requires precision, spatial attention and planning. For example, when we make a diagonal fold, we are working with a bisector; if we fold the paper in half, we explore axial symmetry. As we move on to more complex figures, we introduce concepts such as angles, geometric transformations (rotations, translations and reflections) and even the calculation of areas by comparing the size of the folded parts with the original figure. In the classroom, origami can be used to reinforce learning about plane and three-dimensional geometry. From building a simple figure such as a cube or a fish, to analyzing the properties of the resulting shapes (what figures appear when folded, how many...

Geometry is also beauty, rhythm, and balance, and few spaces reveal this connection as clearly as the world of art. From Islamic art to Cubism, through Renaissance domes and the intricate structures of contemporary art, geometric shapes have been essential tools for artists throughout history. Understanding these forms not only enhances students’ visual analysis skills, but also invites them to discover that mathematics lives beyond the classroom in the colors and shapes of a painting or a sculpture. Cubism revolutionized the way reality was represented. Using geometric figures such as triangles, trapezoids, rectangles, and straight lines, artists broke down objects and faces into planes, allowing viewers to see how geometric forms create depth and multiple perspectives within a single image. Figure 1: Picasso’s Cubism. The golden ratio (proporción áurea) has been used for centuries to achieve visual harmony in paintings, sculptures, and architecture. Figure 2: The golden ratio. Withou...

Learning about geometry involves developing key skills such as spatial awareness, orientation, and the ability to visualize objects from different perspectives. Three-dimensional shapes like cubes, prisms, pyramids, or cylinders offer a fantastic opportunity to foster these skills in the classroom. Understanding 3D figures from a 2D representation is an essential step for students to visualize how a flat shape transforms into a solid object. This kind of thinking is fundamental not only in mathematics but also in areas such as technology, design, architecture, and engineering. One highly effective way to work on this content is through the construction of physical models. Using flat templates that students can cut out, fold, and assemble allows them to concretely experience how a three-dimensional figure comes to life. By handling these templates, children also learn the characteristics of each shape, including concepts like faces, vertices, and edges. Moreover, this activity can be ad...

Geometry is not only used to measure, build, or classify shapes; it can also help us design a more efficient and sustainable world. When we analyze the use of space, materials, and energy from a geometric perspective, we realize that shapes matter… a lot! Why is something designed one way and not another? The shapes of things have a reason, and children should learn to reflect on this. Approaching geometry with a sustainable mindset allows students to understand that math is not just in textbooks: it is also present in the everyday decisions that impact the environment. One of the key principles of sustainable design is optimizing resources, and geometry plays a fundamental role here. A clear example is Tetra Paks, whose rectangular design allows them to be stacked efficiently, without leaving empty spaces, thus reducing volume during transportation and the use of plastic. In other fields, such as architecture or carpentry, the use of geometric patterns allows better use of materials l...