Math Research at Mathzone.io
Embarking on a journey through the fascinating world of math research can uncover a myriad of intriguing concepts and ideas. At mathzone.io, we delve into various math projects that ignite curiosity and inspire further exploration. Whether you’re a seasoned researcher or just getting started, these topics will provide a robust foundation for your next math investigation. Here is a sample of the subjects we cover.
Exploring the Golden Triangle
The Golden Triangle is a captivating subject in the study of sacred geometry. It’s a special isosceles triangle where the ratio of the hypotenuse to the base is the golden ratio, approximately 1.618. This ratio is not only aesthetically pleasing but also appears frequently in nature, art, and architecture. Understanding the properties of the Golden Triangle can lead to deeper insights into the harmony and balance inherent in the natural world. We cover this and more interesting shapes related to the five pointed star.
Unveiling Gabriel’s Horn
Gabriel’s Horn is a fascinating paradox in calculus, also known as Torricelli’s Trumpet. It is formed by rotating the curve y=1/x around the x-axis, extending from x=1 to infinity. Despite having an infinite surface area, it encloses a finite volume. This mind-boggling concept challenges our understanding of geometry and infinity, making it a compelling topic for math analysis. We recently developed a new app so you can work with the intersecting plane of Gabriel’s Horn yourself.
> Gabriel’s Horn Interactive App
The Mystique of the Vesica Piscis
The Vesica Piscis is a fundamental shape in sacred geometry, formed by the intersection of two circles with the same radius. These are positioned in such a way where the center of each circle lies on the circumference of the other. This shape has been revered throughout history for its symbolic significance and mathematical properties. Exploring the Vesica Piscis opens avenues into the study of symmetry, proportion, and the interconnectedness of geometric forms.
Fun Facts About the Number Pi
Pi, approximately 3.14159, is one of the most well-known constants in mathematics. It’s the ratio of a circle’s circumference to its diameter, and its decimal representation is infinite and non-repeating. Pi appears in various equations and mathematical formulas, making it a subject of endless fascination. Did you know that Pi has been calculated to over 31 trillion digits? Delving into the mysteries of Pi can lead to exciting math investigations. Archimedes said that according to his calculations, Pi had upper and lower bounds. We discovered new evidence to support his claim that the upper boundary of Pi is 22/7 in our Squaring the Circle Insights article. We also found another fascinating Pi approximation even closer than this in our Heptagon Seven Pointed Star Geometry article.
Ptolemy’s Theorem and Its Applications
Ptolemy’s Theorem is a powerful tool in the field of trigonometry and geometry. It relates the lengths of the sides and diagonals of a cyclic quadrilateral—a four-sided figure where the vertices lie on the circumference of a circle. This theorem not only provides a method for solving complex geometric problems but also forms the basis for many advanced mathematical concepts. Did you know that Ptolemy’s Theorem can actually Prove the Pythagorean Theorem?
The Enigma of Squaring the Circle
Squaring the circle is a classic problem that has intrigued mathematicians for centuries. The challenge is to construct a square with the same area as a given circle using only a finite number of steps with a compass and straightedge. Although supposedly proven impossible in 1882 (we have some doubts about that), the problem remains a symbol of mathematical creativity and perseverance. We think the problem could have more to do with the mysterious nature of Pi itself. Famous mathematicians like Archimedes and Ramanajun have come up with different values for Pi using different techniques. And these results have been known to correlate in fascinating ways.
Implications of The Kepler Triangle
An interesting definition of the Kepler Triangle is that it’s a right triangle whose edge lengths are the three Pythagorean means of some two numbers. The only triangles in existence for which this is true are the Kepler triangles. In addition, theories about the Great Pyramid of Giza suggest that different proportions might have been used for its construction. One such possibility is known as the Golden Pyramid, which is formed by using a doubled Kepler Triangle as the two perpendicular cross sections of its base.
A New Paradigm In Euclidean Geometry
Math continues to build on itself, and it reveals more of its secrets through the passage of time. We might think of an ancient field like Euclidean Geometry to be thoroughly played out however. Because after all, it’s been around for 2000+ years, so surely all of the low hanging fruit would have already been harvested.
But what if that’s not the case at all, and we’ve only begun to uncover its first layers of mystery? Could most of its secrets still be hiding in the shadows, simply because no one is bothering to look there anymore? We think the answer is yes, and the time has come to pick up where the old math left off. Because newer research by modern visionaries like Frank Chester have blown the entire field wide open again!
We invite you to read our latest article about the Chestahedron Phi Model, where we established a new model which is solely derived from the five pointed star and its inherent golden ratio (or Phi) measurements. We then solidified the legitimacy of this model through mathematical proof. So we didn’t just get the numbers close, we have them exact!
What we ended up with is a miraculous living expression of sacred geometry at its finest, and you can see how the “geometry of the heart” is every bit as mathematically wondrous as you might have suspected!
And this is only the beginning of the journey, since there are plenty of other never before seen shapes like the Chestahedron yet to be discovered. A new breed of geometers will have their work cut out for them — by simply observing this exciting new approach to an ancient Euclidean paradigm! Read more at the links below.
Research Article
> The New Chestahedron Phi Model
New Shape Discovery!
> Star Fort Crystal Geometry & Construction
Beyond The Five Pointed Star
> Heptagon Seven Pointed Star Geometry
Chestahedron Phi Model Press Release PDF
> A New Paradigm In Euclidean Geometry (PDF)
By exploring these captivating math research topics on mathzone.io, you can deepen your understanding of mathematical principles and uncover the beauty and wonder inherent in the world of mathematics. Whether you’re analyzing a divine triangle or investigating circle inversion, each topic offers a unique perspective on the infinite possibilities of math research. We also offer a wide variety of Books and Tools to help with learning more about the fascinating world of math!
Math Research Articles
Chestahedron Seven Sided Geometry
This newly discovered shape is known as the “Chestahedron,” and we think this is one of the most fascinating shapes ever found in mathematics. It’s directly related to all of the platonic solids through a series of transformations, and it was discovered only fairly recently by a man named Frank Chester, who was searching for a seven sided geometry ...
Star Fort Crystal Geometry & Construction
In addition to the venerable Chestahedron, the "Star Fort Crystal" is another significant new discovery created from our folded star fort geometry. We haven't been able to find anyone else referencing even the most fundamental element in a pentagonal star fort construction model however. So we're naming this element a “Pentagonal Triangle.”
Kepler Triangle and Root Phi
The Kepler Triangle is named after the German mathematician and astronomer Johannes Kepler (1571–1630), who wrote about this shape in a 1597 letter. Two concepts that can be used to analyze this triangle, the Pythagorean theorem and the golden ratio, were both of interest to Kepler, who wrote about this shape in a 1597 letter ...
Gabriel’s Horn Intersecting Plane App
Gabriel's Horn Interactive app for evaluating ovoid shapes and circles resulting from setting two points for an intersecting plane. Perform an interactive analysis of the "Painter's Paradox" geometry and see the results. You can also download the oval shapes you create, and the metrics dashboard will keep track of your data...
Vesica Piscis Related Proportions
The Vesica Piscis, sometimes called the "Vesica Pisces," is another one of the more important shapes in mathematics, which is formed by the intersection of two circles with the same radius. The intersection is oriented in such a way that you have the center of each circle lying on the perimeter of the opposite circle...
Squaring The Circle Insights
We have some new insights to share about an age old technique in mathematics called Squaring The Circle. This research was partly inspired by an old illustration we found in a pdf publication written about Viktor Schauberger (1885 - 1958). In Figure 1, we can see how they oriented the squares, circles, and triangles in this particular model ...
Multiplicative Inverse And Gabriel’s Horn
The Multiplicative Inverse is also known as the reciprocal of a number x, denoted by 1/x for all numbers of x not equal to zero. This can be expressed as the reciprocal function y = 1/x, and a graph of this function is shown in Figure 1. Originating from the reciprocal function is a fascinating geometric figure known as Gabriel's Horn ...
Five Pointed Star Reference Shapes
The Five Pointed Star has become a common symbol in Western Culture, most notably introduced on the flag of the United States. But it’s also a very interesting geometric shape which is worthy of further investigation. In Sacred Geometry, one of the most fascinating concepts that intrigues us the most is the Golden Ratio...
Basics of Circle Theorems
Explore the basics of Circle Theorems, essential in understanding circle geometry, discovering key principles, practical applications, and problem-solving techniques. Familiarize yourself with the key terms used in circle geometry ...
Heptagon Seven Pointed Star Geometry
Explore the fascinating world of heptagon geometry, uncovering its unique angles, construction of a seven-pointed star, and diverse applications in design, culture, and education, as well as an interesting relationship to pi ...
Python Number Analytics Library
We wrote a Python script that creates a library of the numbers we want to check against, and then apply an analytics algorithm to check for a variety of possible relationships like equality and divisibility. But we can also check only the decimal portion to see if any familiar patterns emerge ...
Ptolemy’s Theorem And Circle Inversion
In Euclidean geometry, "Ptolemy's theorem" is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus) ...
Publishing Math On Web Pages
We used MathJax for publishing math on web pages. This is fairly easy to set up according to their instructions, and you can refer to their demos page for specific examples. Another great tool to use along with this is MathEQ. This is a builder tool that allows you to visually set up your equations. Then you can simply copy ...
Math Shirts From The Math Zone
Our new Math Zone Shirts are available now! The inspiration for The Math Zone logo design is the "Seed of Life," which is one of the most significant shapes in the history of sacred geometry. The seed of life is constructed with seven intertwining circles, and it was used as a symbol for the seven days of creation ...
