In my blog post “Frégier’s Theorem and Frégier Points” I introduced Fregier’s theorem. In this post I want to show an alternative way of constructing or finding the corresponding Fregier points for points on a Parabola. This alternative method makes use of the Vertex point and the parabola’s axis of symmetry. I am not sure… Continue reading The Vertex, Axis of Symmetry and Corresponding Fregier Points for Parabola Points
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Whittaker’s Root Series: Going Transcendental
Whittaker’s Root Series formula is an interesting method that can be used to calculate the root with the smallest absolute value of a polynomial equation. The formula creates a geometrically convergent infinite series using the determinants of a special class of Toeplitz matrices. These Toeplitz matrices are generated using the coefficients of the polynomial equation.… Continue reading Whittaker’s Root Series: Going Transcendental
Angle Trisection: a Neusis Construction using Lill’s Method and Lill’s Circle
The problem of trisecting an angle using just a compass and a straightedge is an impossible problem. However, the problem of angle trisection can be solved if we are allowed the use of a marked ruler. Geometric constructions that use a marked ruler are called neusis constructions. You can learn more about the topic of… Continue reading Angle Trisection: a Neusis Construction using Lill’s Method and Lill’s Circle
Symbolic Literacy: Justice and the Ostrich
Egyptians were the first to symbolically associate the ostrich with justice. Maat, the goddess of justice, is usually depicted wearing an ostrich feather. The image above shows a scene from the Book of the Dead that depicts the “Weighting of the heart” ritual. In the “Weighting of the heart’ ritual, the heart of of the… Continue reading Symbolic Literacy: Justice and the Ostrich
Discussing a Few of My Favorite Paintings
I am not an artist, but I love art. As an amateur mathematician who is interested in geometry (also Lill’s method), it should not be a surprise that I am interested in visual arts. One of my main hobbies is trying to discover interesting paintings, especially paintings created before 20th century. I am not a… Continue reading Discussing a Few of My Favorite Paintings
2 Interesting Kickstarter Projects
Recently I finally decided to create a Kickstarter account to back up 2 projects that I discovered while browsing the website. My website is too small to help the 2 funding campaigns, nonetheless I want to share a few thoughts about the two projects. The Frogs by Michael Wells “The Frogs” is a point-and-click adventure… Continue reading 2 Interesting Kickstarter Projects
My archive.org Collection
On archive.org I have a small collection of scanned books or brochures. Right now I only have 7 uploads and they are in Romanian or English. For convenience I will embed the scanned materials on this page and maybe I will give a short description. The Dutch and Flemish Cabinet Galleries (National Gallery of Art… Continue reading My archive.org Collection
Lill’s method and the Philo Line for Right Angles
(Note: This is an article from 2016 that I posted on Hubpages. In this article I used Riaz’s way of illustrating Lill’s method. To become more familiar with Lill’s method I recommend going through the links provided in my Lill’s Method page. Also see my Papers page and my Lill’s method articles/posts. ) In this… Continue reading Lill’s method and the Philo Line for Right Angles
Things to Come: Special Drawing Rights, the Petrodollar and The New Economic System
(Note: This is an article that I wrote in 2018 on HubPages ) I believe that in the very near future the world will see some major global transitions. Many of the transitions discussed in this article already started. Right now, most of these transitions are in infancy and below the awareness level of most… Continue reading Things to Come: Special Drawing Rights, the Petrodollar and The New Economic System
Frégier’s Theorem and Frégier Points
Due to the properties of the Frégier point, Frégier’s theorem provides a practical means of constructing with straightedge and square the tangent to a conic at any point on the respective conic. Constructing a Frégier point is very easy and the procedure is the same for any type of conic section (parabola, hyperbola, ellipse or circle). Right… Continue reading Frégier’s Theorem and Frégier Points