If you use scissors and cut out the filled Julia set, you get the first piece of the surface of the eventual 3-D shape. To get the second, DeMarco and Lindsey wrote an algorithm. That algorithm ...

A team of researchers has developed a program that automates the process of figuring out a ... and two-dimensional (2D) structures to have different three-dimensional (3D) shapes.

Material chemists and engineers would love to figure out how to ... or to build 3-D sensors and electronic devices. There have been some successes with simple 3-D shapes such as cubes, but the ...

A cylinder is a 3D shape ... 3^2 + 2 \times \pi \times 3 \times 10 = 78\pi~cm^2 \) (in exact form) or 245 cm 2 (to 3 sig.fig). Notice that the calculation wasn't done until the end. If you work ...

A cylinder is a 3D shape ... 3^2 + 2 \times \pi \times 3 \times 10 = 78\pi~cm^2 \) (in exact form) or 245 cm 2 (to 3 sig.fig). Notice that the calculation wasn't done until the end. If you work ...

Which is curious---because Segerman, 37, has made a career out of visualizing complex mathematical shapes. He is pioneering the use of 3-D printing technology to bring rarefied geometry ...

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another. If you have two flat paper shapes and a pair of scissors, can you cut .

Instead, in 2017, Dr. Yao and her colleagues set out to pattern and build two-dimensional structures that could transform themselves into three-dimensional shapes. “We were thinking edible ...

A key question that remains in biology and biophysics is how three-dimensional tissue shapes ... wanted to find out how this shape change occurs. "To explain this process, we drew inspiration ...