Relating six properties of a triangle in one equation

Let a, b, and c be the sides of a triangle. Let p be perimeter of the triangle. Let r be the radius of the largest circle that can be inscribed in the triangle, and let R be the radius of the circle through the vertices of the triangle. Then

Preprocessing text to make it more compressible

Repetitive text compresses efficiently. Text like the lyrics to Jingle Bells ought to compress more efficiently than ordinary prose, assuming the compression algorithm can exploit the repetition. The idea of the Burrows-Wheeler transform is to permute text in before compressing it. The hope is that the permutation will make the

Chris’ Corner: There is a Turtle at the Bottom

If you were in charge of the curriculum at a college teaching web development, would you ensure the curriculum was regularly updated with bleeding edge technology? Or would you establish a slower moving curriculum with tried and true technologies? That’s tough. You can’t just flip a coin. It may be

What launching rockets taught this CTO about hardware observability

Austin Spiegel, CTO and co-founder of Sift, tells Ben and Ryan about his journey from studying film to working at SpaceX to founding Sift. Austin shares his perspective on software development in high-stakes environments, the challenges of hardware observability, and why paranoia is valuable in safety-critical engineering. Bonus story: Austin

Why does FM sound better than AM?

The original form of radio broadcast was amplitude modulation (AM). With AM radio, the changes in the amplitude of the carrier wave carries the signal you want to broadcast. Frequency modulation (FM) came later. With FM radio, changes to the frequency of the carrier wave carry the signal. I go

Shifted reciprocal

It’s interesting to visualize functions of a complex variable, even very simple functions like f(z) = 1/z. The previous post looked at what happens to triangles under the reciprocal map w = 1/z. This post will look at the same map applied to a polar grid, then look at the

7 Best Python Certifications For All Levels [2024 Update]

Triangles to Triangles

The set of functions of the form f(z) = (az + b)/(cz + d) with ad ≠ bc are called bilinear transformations or Möbius transformations. These functions have three degrees of freedom—there are four parameters, but multiplying all parameters by a constant defines the same function—and so you can uniquely

Is this the real life? Training autonomous cars with simulations

Ben Popper interviews Vladislav Voroninski, CEO of Helm.ai, about unsupervised learning and the future of AI in autonomous driving. They discuss GenAI’s role in bridging the gap between simulation and reality, the challenges of scaling autonomous driving systems, the commercial potential of partial autonomy, and why software is emerging as

9 Best Linux Certifications in 2024 (Updated Guide)