Author Archives: hinhoc

About hinhoc

To discover new interesting: first observe all strange, abnormal but then make them familiar, normal!

Finite and infinite regions defined by n lines in the plane

It is well known result in plane geometry: The maximum number of regions defined by n lines in the plane is R(n) = n(n+1)/2 +1. Of course, there are not any parallel pair from these lines. All sets of lines discussed here covers this … Continue reading

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Using sum of squares triangle to prove sum of squares formula

We construct a number triangle from the integers 1, 2, 3, . . . n as follows. The first column contains 2*n-1 integers 1. The second column contains 2*n-3 integers 2. . . The last column contains only one integer … Continue reading

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New property of Bui chord circles – Tính chất mới của đường tròn dây cung Bui

November 12, 2011 Alexander Bogomolny published in Cut The Knot my “Pair of Siblings to Archimedes’ Twins“: http://www.cut-the-knot.org/Curriculum/Geometry/ArbelosBui.shtml (*) This pair later is collected by Floor van Lamoen in Online catalogue of Archimedean circles and named as “Bui chord circles“: … Continue reading

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Proof of Jo Niemeyer’s construction using Kurt Hofstetter’s construction – Chứng minh phép dựng Niemeyer dùng phép dựng Hofstetter

In “A simple construction of the golden section”, Forum Geometricorum, 11 (2011) 53: http://forumgeom.fau.edu/FG2011volume11/FG201105index.html Jo Niemeyer offered a beautiful way of constructing the Golden Ratio with three equal segments. It is interesting that Jo Niemeyer’s construction can be proved by … Continue reading

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Golden Ratio in Parabola – Tỷ Số Vàng trong Parabola

Point E is orthogonal projection of focus F on directrix of a parabola. The circle with diameter EF intersects the parabola at two points A, B. Results: Common chord AB divides diameter EF by golden ratio and of course AEF … Continue reading

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Triangle Classification Diagram – Sơ đồ Phân loại Tam giác

In CTK arcticle Triangle Classification there is one interesting diagram of H. R. Jacobs. In one rectangle it represents all seven kinds of triangles of all classifications. I like it so much. I slightly change it to get one fixed … Continue reading

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When I die…

When I die…  two points still make a line The constant distance still makes a circle The trilinears and the barycentrics Are still used on triangle center sites. When I die…  something is still mine! Khi tôi chết… hai điểm … Continue reading

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