Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack n unit circles into the smallest possible equilateral triangle. Optimal solutions are known for n < 13 and for any triangular number of circles, and conjectures are available for n < 28. A conjecture of Paul ErdΕs and Norman Oler states that, if n is a triangular number, then the optimal packings of n β 1 and of n circles have the same side length: that is, according to the conjecture, an optimal packing for n β 1 circles can be found by removing any single circle from the optimal hexagonal packing of n circles. This conjecture is now known to be true for n β€ 15. Minimum solutions for the side length of the triangle: A closely related problem is to cover the equilateral triangle with a fixed number of equal circles, having as small a radius as possible. (Wikipedia).
How To Construct An Equilateral Triangle
Complete videos list: http://mathispower4u.yolasite.com/ This video will show how to construct an equilateral triangle with a compass and straight edge.
From playlist Triangles and Congruence
Constructing the Circumcircle of an Equilateral Triangle
This video shows how to construct the circumcircle of an equilateral triangle. The steps are: 1. Construct an equilateral triangle (keep the compass the same length). 2. Construct the perpendicular bisector of any two sides. 3. Set the compass to the length of the circumcenter (created
From playlist Geometry
How do you find all of the sides for a equilateral triangle
π Learn how to find the missing side of a triangle. A triangle is a polygon with three sides. Triangles are classified on the basis of the angles or on the basis of the sides. The classification of a triangle on the basis of the sides are: scalene, isosceles, and equilateral triangles. A
From playlist Triangles
How to find the measure of each side of an equilateral triangle
π Learn how to find the missing side of a triangle. A triangle is a polygon with three sides. Triangles are classified on the basis of the angles or on the basis of the sides. The classification of a triangle on the basis of the sides are: scalene, isosceles, and equilateral triangles. A
From playlist Triangles
What is an equilateral triangle
π Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
The math that solves social distancing (& lots more)
This is my first ever upload, which I created as a submission to the "Summer of Math Exposition 1" (SoME1) contest. I apologize sincerely for the poor audio quality. I promise to improve this the next time around! Here are all the links I promised during the video: Katie Steckles's blog
From playlist Summer of Math Exposition Youtube Videos
Reuleaux Triangles - GCSE Higher extension
Proving the area and perimeter of a Reuleaux triangle. Mathologer video on shapes of constant width (really awesome!) - https://youtu.be/-eQaF6OmWKw
From playlist Geometry Revision
Equilateral triangle inside a circle problem
Finding the radius given the side length of a circumscribed equilateral triangle. If you found this interesting, you might like Reuleaux triangles - https://www.youtube.com/watch?v=aDRmbLHyq8A
From playlist Problem Solving
Rigidity of the hexagonal triangulation of the plane and its applications - Feng Luo
Feng Luo, Rutgers October 5, 2015 http://www.math.ias.edu/wgso3m/agenda 015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year
From playlist Workshop on Geometric Structures on 3-Manifolds
New Geometry Tool! Construct an Equilateral Triangle
Thrilled to share my new tool for geometry that is safer, easier to use and more accurate than a compass. Here I show how to construct an equilateral triangle using a circle arc template and a straightedge. ENJOY! Recent article about it here https://www.aimsciences.org/article/doi/10.393
From playlist Learning Geometry with a Circle Arc Template
How to Construct a Line Segment of Given Length Using a Circle Arc Template
Thrilled to share my new tool for geometry that is safer, easier to use and more accurate than a compass. Here I show how to construct a given line segment from a given point using a circle arc template and a straightedge. ENJOY! Recent article about it here https://www.aimsciences.org/ar
From playlist Learning Geometry with a Circle Arc Template
New Geometry Tool! Construct a Perpendicular Through a Point on a Line
Thrilled to share my new tool for geometry that is safer, easier to use and more accurate than a compass. Here I show how to construct a perpendicular line through a given point on a line using a circle arc template and a straightedge. ENJOY! Recent article about it here https://www.aimsc
From playlist Learning Geometry with a Circle Arc Template
How to Construct the Midpoint of a Line Segment
Thrilled to share my new tool for geometry that is safer, easier to use and more accurate than a compass. Here I show how to construct the mid point of a given line segment using a circle arc template and a straightedge. ENJOY! Recent article about it here https://www.aimsciences.org/arti
From playlist Learning Geometry with a Circle Arc Template
How to do geometry with a short ruler! Construct a normal / perpendicular line
Thrilled to share my new tool for geometry that is safer, easier to use and more accurate than a compass. Here I show how to construct a normal (perpendicular) line using a circle arc template and a straightedge of fixed length. ENJOY! Recent article about it here https://www.aimsciences.
From playlist Learning Geometry with a Circle Arc Template
AQA GCSE Maths Foundation (8300) : Practice Set 2 Paper 2
A run-through of AQA's GCSE Maths Foundation Paper 2 from Set 2 of the practice paper releases. Click on the hyperlinks in this description below to skip straight to individual questions. If you're watching on a mobile device, you may need to click the hyperlinks I've attached in the vid
From playlist AQA (8300) Foundation Tier Exam Solutions
How to determine all of the measure of angles for an equilateral triangle
π Learn how to find the missing side of a triangle. A triangle is a polygon with three sides. Triangles are classified on the basis of the angles or on the basis of the sides. The classification of a triangle on the basis of the sides are: scalene, isosceles, and equilateral triangles. A
From playlist Triangles
What is an equiangular triangle
π Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Ex: Find the Perimeter of an Equilateral Triangle Given the Area without Trigonometry
This video explains how to determine the perimeter of an equilateral triangle given the area with out using trigonometry. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Applications of Quadratic Equations
Find the measure for the sides of an equilateral triangle
π Learn how to find the missing side of a triangle. A triangle is a polygon with three sides. Triangles are classified on the basis of the angles or on the basis of the sides. The classification of a triangle on the basis of the sides are: scalene, isosceles, and equilateral triangles. A
From playlist Triangles
Margaret Kepler - 4 x13 - G4G13 Apr 2018
A progress report on my project to design a deck of playing cards with "mathy" concepts.
From playlist G4G13 Videos