A Difficult Geometry Puzzle
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…
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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
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Harmonic triangle
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…
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A generalization of the Pythagorean theorem
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…
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LaTeX package for Pascal-like triangles
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…
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SmApiCreatePlanarCircle#
crOrigin – [in ]: Position of bottom left corner of plane dRadius – [in ]: Radius of circle rpResult – [out]: Resulting SmBrep
Mysteries of Fractals: Infinite Patterns in Nature & Mathematics
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…
Hexagon build reaches new milestone in Minster Quarter transformation
A new walkway has been put in place in the latest milestone of the rejuvenation of Reading's iconic theatre this week. Picture: Reading Borough Council Teams are continuing the work to transform The Hexagon theatre in central Reading, with the…
The Counterintuitive Geometry Problem That Tripped Up 90% of Readers
Read the previous blog: The Equation That Broke My Brain (And the Elegance That Fixed It) Imagine wrapping a piece of rope tightly around the equator of the Earth. Now, imagine you want to lift that rope exactly one foot…
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Astraeus: The Mysterious Child Who Stared at the Sun and Grew Up With Pythagoras
Pythagoras is best known for the famous theorem that bears his name, one of the fundamental principles of geometry. However, far fewer know that the man behind it belonged to a tradition in which mathematics and magic were not always…