Times Tables, Mandelbrot and the Heart of Mathematics
Mathologer・2 minutes read
The text discusses creating circular representations of times tables, showcasing patterns like the cardioid and nephroid curves based on multiplication results. These curves can be found in mathematical contexts such as rolling curves, coffee cup reflections, and the Mandelbrot set, with the number of petals corresponding to the times table explored.
Insights
- The circular times tables images showcase mathematical patterns like the cardioid and nephroid, which appear in diverse contexts such as rolling curves, coffee cups, and the Mandelbrot set.
- By exploring multiplication factors within modular arithmetic, unique shapes emerge, with the number of petals in these curves directly corresponding to the specific times table being examined, leading to a variety of intriguing patterns beyond the cardioid and nephroid.
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Recent questions
How are times tables represented in a circular form?
By placing points around a circle and connecting them.
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Summary
00:00
Circular Times Tables Create Mathematical Patterns
- The images provided are of times tables represented in a circular form.
- To create these images, start with a circle and place points around the perimeter, labeling them with numbers.
- Begin with the two times table, connecting the points based on the multiplication results.
- The connections form patterns like the cardioid, a heart-shaped curve found in various mathematical contexts.
- The cardioid can be seen in rolling curves, conical coffee cups, and the Mandelbrot set.
- Exploring the three times table reveals the nephroid, a kidney-shaped curve, also present in the Mandelbrot set and coffee cup reflections.
- The number of petals in these curves corresponds to the times table being explored.
- Continuously increasing the multiplication factor leads to transformations from the cardioid to the nephroid and beyond.
- The concept of modular arithmetic, specifically the times table modulo 200, produces various patterns, including the cardioid and other intriguing shapes.
