A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for n is given by the formula Thus, the first few centered decagonal numbers are 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, ... (sequence in the OEIS) Like any other centered k-gonal number, the nth centered decagonal number can be reckoned by multiplying the (n − 1)th triangular number by k, 10 in this case, then adding 1. As a consequence of performing the calculation in base 10, the centered decagonal numbers can be obtained by simply adding a 1 to the right of each triangular number. Therefore, all centered decagonal numbers are odd and in base 10 always end in 1. Another consequence of this relation to triangular numbers is the simple recurrence relation for centered decagonal numbers: where (Wikipedia).
Sketch the angle then find the reference angle
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
Find the reference angle of a angle larger than 2pi
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
Using midpoint formula find the midpoint between two coordinates ex 2, C(-2, 7), D(-9, -5)
👉 Learn how to find the midpoint between two points. The midpoint between two points is the point halfway the line joining two given points in the coordinate plane. To find the midpoint between two points we add the x-coordinates of the two given points and divide the result by 2. This giv
From playlist Points Lines and Planes
How to determine the reference angle of an angle in degrees
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
How to find the reference angle of an angle larger than 2pi
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
Learning to find the reference angle by using coterminal angle
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
Find the reference angle of a negative angle
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
J. Smillie - Horocycle dynamics (Part 2)
A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include: * SL_2(R) orbit closures and inva
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Find the midpoint between two points w(–12,–7), T(–8,–4)
👉 Learn how to find the midpoint between two points. The midpoint between two points is the point halfway the line joining two given points in the coordinate plane. To find the midpoint between two points we add the x-coordinates of the two given points and divide the result by 2. This giv
From playlist Points Lines and Planes
Use Proportions to Solve Applications (No Cross Products)
This video explains how to use ratios and rates to form proportions to solve applications problems
From playlist Number Sense - Decimals, Percents, and Ratios
Debora Coombs - Raising Penrose - G4G13 Apr 2018
Raising Penrose tiling into a dimension of somewhere between two and five dimensions.
From playlist G4G13 Videos
How to Construct an Icosahedron
How the greeks constructed the icosahedron. Source: Euclids Elements Book 13, Proposition 16. In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces. https://www.etsy.com/lis
From playlist Platonic Solids
ASVAB Practice Test 1 Mathematics Knowledge
In this video, I go through the ASVAB Practice Test 1 Mathematics Knowledge section. The concepts covered in this section include geometry, angles formed by intersecting lines, decimals, fractions, mixed numbers, improper fractions, percents, integers, exponents, converting units of measur
From playlist ASVAB Math Practice
Finding Interior and Exterior Angles in a Polygon
Learn how to find the Interior and Exterior Angles of a Polygon in this free math video tutorial by Mario's Math Tutoring. We discuss regular and nonregular polygons and go over the forumulas as well as example problems. 0:21 Formula for the Sum of Interior Angles in a Polygon 1:14 Formul
From playlist Geometry
Roger Penrose - Forbidden crystal symmetry in mathematics and architecture
Sir Roger Penrose provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of non-repeating patterns in design and architecture. It is a rigorous mathematical theorem that the only crystallographic symmetries are 2-fold, 3-fold, 4-fold, and 6-fold s
From playlist Mathematics
Group theory 13: Dihedral groups
This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.
From playlist Group theory
NAMING POLYGONS | What is the name of 69 sided polygon?
#namingpolygons #mathlesson #brainfeeding
From playlist Summer of Math Exposition Youtube Videos
Find the reference angle and sketch both angles in standard position
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
P. Apisa - Marked points in genus two and beyond
In the principal stratum in genus two, McMullen observed that something odd happens - there is only one nonarithmetic Teichmuller curve - the one generated by the decagon. This strange phenomenon begets another - a primitive translation surface in genus two admits a periodic point that is
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Find the reference angle and sketch both angles in standard position
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle