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Today's log begins with a question for Copilot.shu: This diagram was in a certain book. I believe it is likely a diagram related to geometric analysis, but since I have never received a proper explanation or known its original…
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The 358-Year Mystery of Fermat's Last Theorem The theorem stated that a^n+b^n≠c^n, for all n≥3, a,b,c and n are integers To appreciate the … Fermat's Lat Theorem: A Million Dollars Problem. The 358-Year Mystery…
A regular hexagon PQRSTU is inscribed in a circle of radius 5. A point X on the circumference of the circle is connected to the vertices of the hexagon to form six chords X P, XQ, X R, X S, XT…
EurekAlert! Ahmed Mostafa Abdelhady and Kazumitsu Onizuka, Tohoku University. Reporters may freely use these materials in news coverage with appropriate credit information. More on this News Release New labeling tool uncovers hexokinase-1 as a G-quadruplex binding protein
Pascal’s triangle is the most famous triangular arrangement of numbers. I’ve written about other numerical triangles, such as Bell’s triangle and the trinomial triangle. There’s another well-known triangle that somehow I never heard of until recently: the harmonic triangle, first…
G. D. Chakerian [1] discovered the following generalization of the Pythagorean theorem. Take any triangle and attach squares to each side. From each triangle vertex, extend a line perpendicular to the opposite side and extend the line through the square, as shown in…
When I wrote about the harmonic triangle yesterday, I displayed the triangle left-aligned using fixed-width text because that was easier than producing the format you usually see for Pascal’s triangle and related triangles. I asked Claude to write a LaTeX…
crOrigin – [in ]: Position of bottom left corner of plane dRadius – [in ]: Radius of circle rpResult – [out]: Resulting SmBrep
This article will dive into the world of fractals, exploring their properties, how they are generated, and their presence in our world. Fractals are mathematical sets showing a repeating pattern that displays at every scale. They are known for their…