Math Behind Shadow Art
MATH S2 FINAL PROJECT DOCUMENTATION
Angela Wang & Miji Kim
Objectives
The primary objective of this project is to elucidate the concept of transformations in mathematics through the lens of art. Students will gain hands-on experience with different types of transformations including translation, rotation, reflection, and dilation. By engaging in artistic creation, students will grasp the essence of these transformations and how they alter the appearance and structure of objects.
Project Components
1. Understanding Transformations:
• Begin by introducing students to the fundamental transformations in mathematics. Explore each transformation type through interactive demonstrations and real-life examples. Discuss the key characteristics and properties of each transformation.
2. Artistic Exploration:
• Encourage students to unleash their creativity by integrating mathematical transformations into their artwork. Provide a variety of artistic mediums such as painting, drawing, sculpture, or digital art. Challenge them to experiment with different techniques to depict transformations visually.
3. Transformational Art Gallery:
• Culminate the project with a transformational art gallery showcasing students’ creations. Invite peers, teachers, and parents to appreciate the fusion of mathematics and art. Encourage students to articulate the mathematical concepts behind their artwork, fostering communication and critical thinking skills.
4. Reflective Analysis:
• Facilitate reflective discussions where students analyze their artwork in the context of mathematical transformations. Encourage them to identify and articulate the specific transformations portrayed in their pieces. Discuss the creative process and how mathematical concepts influenced their artistic decisions.
Learning Outcomes
Through active participation in this transformational art project, students will:
• Gain a deep understanding of mathematical transformations and their applications in art.
• Develop creative problem-solving skills by integrating mathematical concepts into artistic expression.
• Enhance visual-spatial reasoning abilities through hands-on exploration of transformations.
• Foster appreciation for the interconnectedness of mathematics and the arts, fostering
interdisciplinary thinking.
This transformational art project serves as a platform for students to explore, create, and
appreciate the beauty of mathematics in the realm of art. By merging analytical thinking with
creative expression, students embark on a journey of discovery, unlocking new perspectives
and insights into the enchanting world of transformations. Let’s embark on this transformative
adventure together!
Process
Our group decided to do shadow art. After deciding what project we should work on, we each chose a picture we should carve out for the shadow art. The chosen pictures were:
In order to carve it out easily we made the picture white and black. Then, we made the contrast between the white and the black part as high as we could so that we could know where to carve out without getting confused. However, we went through a lot of iterations and errors to finish this project.
Iterations:
Our initial idea was to stick the printed-out picture on the cardboard and carve the white part out since the black is the shadow. However, the cardboard was hard to cut which was different from our expectation, and we made some mistakes throughout carving them out.
The cardboard was not cutting well and the reflection didn’t look very accurate compared to the picture. To fix this problem, our group practiced how to see the parts where we should carve out so that we could reduce mistakes when we were carving.
Initial Carving Attempt
Upon initial practice, we endeavored to carve the image directly onto the cardboard surface, guided by our preparatory method. However, despite our knowledge of the intended cutting areas, the process of precisely excising the cardboard while maintaining the overlaid image proved challenging.
Revised Approach
Consequently, we opted for an alternative technique to create the desired facial carvings. This revised approach involved manually rendering the facial features onto the cardboard surface and shading the areas intended to remain uncarved. Employing this method, we successfully carved the drawings with a satisfactory level of accuracy, albeit with a degree of imprecision. Upon reflecting the carved surface with light, the resulting image bore a recognizable resemblance to the reference picture.
Understanding Light and Shadow
While one aspect of our carved drawing appeared consistent from various lighting angles, achieving an accurate representation of the other side necessitated a comprehensive understanding of the interplay between light and shadow. To precisely capture the carved facial features, we had to account for the inverse relationship between proximity to the light source and the perceived size of the cast shadow. Specifically, areas closer to the light required more intricate detailing, as their shadows would appear magnified upon projection, in contrast to the relatively diminutive shadows cast by regions farther from the light source.
Applying the Inverse Square Law
Comprehending the mechanisms governing shadow and light, we strategically reduced the scale of one facial region and positioned it in closer proximity to the light source. This deliberate manipulation ensured that the projected shadow’s dimensions corresponded proportionally to the frontal facial features.
Importance of Lighting Angle
However, if the lighting angle is not properly adjusted, the reflected projection of the carved drawing becomes distorted, compromising its intended representation.
Achieving Accurate Projection
To accurately capture the desired imagery, it is imperative to precisely calibrate the angle of the light source. This angular adjustment facilitates the appropriate lighting conditions, preventing distortions in the cast shadows and ensuring a faithful reflection of the carved artwork.
Videos of the Outcome
Please click on the following link to view the final outcome of the shadow art project:
Mathematical Connection
Geometric:
After finishing the project itself, we searched for some math-related reasons behind shadow art. We both agreed that one reason would be geometry and shapes because, during the process, we used shapes like circles, squares, or triangles to create the patterns or designs we wanted. Thus, understanding the geometric relationships will help us construct the end result more visually appealing and balanced.
Proportional and Positioning:
One additional thing we found is that perspective is significant to this project. We both found out that perspective is important when creating shadow art since we focused either on a one-point perspective or a two-point perspective to depict the way the object will appear in the three-dimensional space. The size and shape of a shadow are directly proportional to the size and shape of the object reflecting the shadow, as well as the angle and distance of the light source. Understanding these proportional relationships is significant for shadow art to control the scale and distortion of shadow creations. As the position of the light source changes, the length and direction of the shadow change proportionally. For example, when we didn’t find the right position for the light, our reflection in the shadow was distorted. However, if we find the right position for the light, the drawing is properly displayed.
Inverse Square Law:
The inverse square law is a mathematical theory that defines how light intensity decreases as distance changes from the source. This law directly impacts the clearness and appearance of shadows in shadow art. As the distance between a light source and an object increases, the shadows reflected by that object become softer and more unclear due to the inverse square law. This is because the light rays are spreading out wider, resulting in a more gradual transition from light to shadow. Conversely, when the light source is closer to the object, the shadows become more clear, with sharper edges. This is due to the light rays being more concentrated and intense near the source. We utilized this law by carving some parts of the drawing smaller than the other and placing them closer to the light source.
