Geometry – Cantor's Archive
Geometry
Horrocks’ Measurements of How Far Away The Sun Is
Understanding the sun-to-planets absolute distances was a long-run investigation proceeding with new scientific-tools and new laws. As a police case requires time and symmetry of action that concatenates all threads within one bracket, space exploration is alike. At the time of Venus transit in 1761, scientists had all to kill
Discrete Mathematics
How Many Distances Must Be Made from N Points?
My most striking contribution to geometry is, no doubt, my problem on the number of distinct distances. This can be found in many of my papers on combinatorial and geometric problems. -Paul Erdős, On Some of My Favorite Theorems, 1996. Erdős is one of the greatest mathematicians from history, and
Geometry
Visualizing Mathematical Equations and Operations
Capture the Essence of an Equation and Solve it Visually by Using Mathematical Graphs
Geometry
Understanding Perpendicular Lines and Orthogonal Trajectories
When two lines are perpendicular (or orthogonal) with each other, it means they form a 90° angle when they intersect. If you were taught about perpendicular lines in Algebra or for the SAT, you were probably forced to memorize something like “the slope of the perpendicular line is the negative
Geometry
Cubic Polynomials – Using Similar Triangles to Approximate Roots
Applying Similar Triangles to approximate roots aided by ‘natural’ Cubic architecture
Puzzle
Heron’s Shortest Path Problem
Which path minimizes the distance needed to get water and then transport it to the green village?
Geometry
Geometrical Beauty: The Properties of the Tautochrone Curve
When a Sliding Bead at Rest Reaches Its Minimum Independently of Its Where It Started
Geometry
To 3D and Beyond
How many spatial dimensions do we live in? How many can we directly perceive? Are the two answers the same? If they are different, what effect, if any, do any higher dimensions have on us?
Geometry
How Geometry and Combinatorics Tame the Networks in your Brain
Physical Constraints Regulate Information Dynamics
Differential Geometry
The Gauss Bonnet Theorem and an Introduction to Spherical Geometry
A visual introduction to Spherical geometry, a geometry where triangles’ angles don’t sum to 180.
Geometry
The Hidden Life of Circles
Everyone knows that circles are quite simple figures, but from the perspective of number theory they have many secrets inside.
Geometry
The Law of Sines with Proof
It states that the ratio of any side to the opposite sine in a given triangle has a constant value.