Jakob Steiner, born in 1796 and dying in 1863, was a Swiss mathematician known for his contributions to geometry, particularly in the field of synthetic geometry. He is often recognized for his work in projective geometry and for introducing certain methods and concepts that are foundational in the study of curves and surfaces. Steiner is best known for Steiner conics, which relate to the properties of conic sections, and for his work on geometric constructions that utilize only straightedge and compass.
Olry Terquem is a notable figure in the field of mathematics, particularly known for his contributions to the theory of numbers and mathematical logic in the 19th century. He was a French mathematician born in 1810 and passed away in 1895. Terquem is recognized for his work on prime numbers and his investigations into mathematical properties and sequences. His research has remnants in academic discussions related to number theory and the foundations of mathematics.
Tom Hull is a mathematician known for his work in the field of mathematics and education. He is particularly recognized for his contributions to the study of mathematical patterns, geometry, and recreational mathematics. Hull has also been involved in developing materials for mathematical education and promoting mathematical problem-solving skills. He is perhaps best known in the context of his work with origami and the mathematical principles that govern the art of paper folding.
Robert Finn is an American mathematician known for his contributions to the field of mathematics, particularly in the areas of partial differential equations and applied mathematics. He has made significant advancements in mathematical analysis and has published numerous papers and articles in his areas of expertise. Finn is also known for his work as an educator and has held various academic positions, including professorships at prominent universities. Additionally, he has authored textbooks and monographs that are widely used in the study of mathematics.
Sumner Byron Myers is a name associated with multiple individuals, but it is most commonly recognized in the context of an American mathematician known for his work in mathematical logic and computational theory.
The camera matrix is a fundamental concept in computer vision and graphics, specifically in the context of camera modeling and image formation. It is a mathematical representation that describes the intrinsic and extrinsic parameters of a camera. ### Components of the Camera Matrix 1. **Intrinsic Parameters**: These parameters relate to the internal characteristics of the camera. They include: - **Focal Length (fx, fy)**: Determines the scale of the image and is usually expressed in pixel units.
A border barrier is a physical structure, such as a wall or fence, that is built along a national border to control the movement of people, animals, and goods between countries. These barriers are often constructed with the intention of enhancing national security, preventing illegal immigration, and reducing smuggling or trafficking activities. Border barriers can vary in design, materials, and height, depending on the geographic and political context.
The Essential matrix is a key concept in computer vision and 3D geometry, specifically in the context of stereo vision and structure from motion. It encodes the intrinsic geometry between two views of a scene captured by calibrated cameras. The Essential matrix relates corresponding points in two images taken from different viewpoints and is used to facilitate the recovery of the 3D structure of the scene and the relative poses (rotation and translation) of the cameras.
In computer vision, homography refers to a transformation that relates two planar surfaces in space, allowing one to map points from one image (or perspective) to another. More specifically, it describes the relationship between the coordinates of points in two images when those images are taken from different viewpoints or perspectives of the same planar surface.
The great icosahedral 120-cell (also known as the great icosahedron or the 120-cell) is a four-dimensional polytope, belonging to the family of regular polytopes. It is one of the six convex regular 4-polytopes known as the "4D polytopes," and it is specifically classified as a regular 120-cell.
A snub dodecahedral prism is a type of three-dimensional geometric shape that can be classified as a prism. More specifically, it is constructed by taking a snub dodecahedron as its base and extending that shape vertically to form the prism. ### Characteristics of a Snub Dodecahedral Prism: 1. **Base Shape**: The snub dodecahedron is a convex polyhedron with 12 regular pentagons and 20 equilateral triangles.
The stellated rhombic dodecahedral honeycomb is a three-dimensional arrangement of space-filling cells that composed of stellated rhombic dodecahedra. A honeycomb, in geometrical terms, refers to a structure comprised of repeating units that completely fill space without any gaps. In the case of the stellated rhombic dodecahedral honeycomb, the basic unit cell is a stellated rhombic dodecahedron.
A truncated dodecahedral prism is a type of geometric solid that is a combination of two distinct shapes: a truncated dodecahedron and a prism. To break it down: 1. **Truncated Dodecahedron**: This is a convex polyhedron with 12 regular pentagonal faces, where each vertex of the original dodecahedron has been truncated (flattened) to create additional faces.
A truncated tetrahedral prism is a three-dimensional geometric shape that is formed by extending a truncated tetrahedron along a perpendicular axis to create a prism. To clarify each component: 1. **Truncated Tetrahedron**: This is a type of polyhedron that results from truncating (or cutting off) the corners (vertices) of a regular tetrahedron.
A stellation diagram is a graphical representation used in geometry, particularly in the study of polyhedra. Stellation refers to the process of extending the faces, edges, or vertices of a polyhedron to create new shapes. The result is often a more complex, star-like structure, which is why it's called "stellated" (from the Latin word "stella," meaning "star").
Uniform coloring typically refers to a type of coloring in various fields such as graph theory, mathematics, and computer science, where a certain uniformity is applied to how objects (like vertices or regions) are colored according to specific rules or criteria.
In complex geometry, theorems often pertain to the study of complex manifolds, complex structures, and the rich interplay between algebraic geometry and differential geometry. Here are some important theorems and concepts in complex geometry: 1. **Kodaira Embedding Theorem**: This theorem states that a compact Kähler manifold can be embedded into projective space if it has enough sections of its canonical line bundle. It is a crucial result linking algebraic geometry with complex manifolds.
The Collage Theorem, often referred to in the context of topology and geometry, is a concept related to the study of spaces and continuous functions. However, the term "Collage Theorem" may not be universally recognized under that name in all areas of mathematics, and its interpretation can vary depending on the context.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.Figure 4. Visual Studio Code extension tree navigation.Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact





