A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers. The centered octagonal numbers are the same as the odd square numbers. Thus, the nth odd square number and tth centered octagonal number is given by the formula The first few centered octagonal numbers are 1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225 Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number. is the number of 2x2 matrices with elements from 0 to n that their determinant is twice their permanent. (Wikipedia).
8.01x - Module 10.01 - Circular orbit of satellite around Earth.
Circular orbit of satellite around Earth. What is its period?
From playlist 8.01x - MIT Help Sessions
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Geometry - Basic Terminology (29 of 34) What Are Inscribed Angles?
Visit http://ilectureonline.com for more math and science lectures! In this video I will define and gives the formula of inscribed angles. Next video in the Basic Terminology series can be seen at: http://youtu.be/zn5eRO_T15Q
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
Determining the volume of rectangular pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
Geometry - Basic Terminology (30 of 34) Using Inscribed Angles to Find the Angle
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the angles (inside a circle) using the inscribed angle formula. Next video in the Basic Terminology series can be seen at: http://youtu.be/L2L-WoL7fo4
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
SQUARE TO OCTAGON convert the easy way 0.41421 online calculator
Making an octagon is is very easy if you start with a true square. Simply multiply your WIDTH (x) 0.41421 and that is your edge length. Here is the rest of my formula. http://www.greenpowerscience.com/OCTAGONCAL.html 0.41421 = EDGE LENGTH 0.29291 = PUP LENGTH 0.54119 = OCTAGON CENTER Squ
From playlist Woodworking like a Boss
Geometry: Ch 4 - Geometric Figures (15 of 18) The Right Circular Cone
Visit http://ilectureonline.com for more math and science lectures! In this video I will define the right circular cone, and explain the equations of its surface area and volume. Next video in this series can be seen at: https://youtu.be/QTuyo-_2iTQ
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
How to find the volume of a pentagonal pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
Ex 1: Find Standard Equation of a Circle Given the Endpoints of a Diameter
This video provides an example of how to find the standard equation of a circle given the endpoints of a diameter. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Circles
AlgTop21: The two-holed torus and 3-crosscaps surface
We describe how the two-holed torus and the 3-crosscaps surface can be given hyperbolic geometric structure. For the two-holed torus we cut it into 4 hexagons and then describe a tesselation of the hyperbolic plane (using the Beltrami Poincare model described in the previous lecture) compo
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Maths Olympiad - UKMT Cayley 2022 Q4
Working through Question 4 of the UKMT Cayley (Intermediate) Maths Olympiad paper from 2022 The Cayley Olympiad is usually sat by students in Year 9 in England and Wales (age 13-14) who have done very well in the Intermediate Maths Challenge. Free courses: Intermediate Olympiad: https://
From playlist UKMT Intermediate Olympiad
The Beauty of Symmetry: An Introduction to the Wallpaper Group
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription! Resources used in the video: Web app to generate all 17 wallpapers: https://math.hws.edu/eck/js/symmetry/wallpaper.html Lots of i
From playlist Cool Math Series
13. The Prince and the Palace: Human Made Divine on the Palatine Hill
Roman Architecture (HSAR 252) Professor Kleiner investigates the major architectural commissions of the emperor Domitian, the last Flavian emperor. She begins with the Arch of Titus, erected after Titus' death by his brother Domitian on land previously occupied by Nero's Domus Transitor
From playlist Roman Architecture with Diana E. E. Kleiner
11. Notorious Nero and His Amazing Architectural Legacy
Roman Architecture (HSAR 252) Professor Kleiner features the architecture of Augustus' successors, the Julio-Claudian emperors, whose dynasty lasted half a century (A.D. 14-68). She first presents Tiberius' magnificent Villa Jovis on the Island of Capri and an underground basilica in Ro
From playlist Roman Architecture with Diana E. E. Kleiner
Calculus 2: Polar Coordinates (1 of 38) What are Polar Coordinates?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what are polar coordinates and Cartesian coordinates. The Cartesian coordinates use x and y to locate a point on a plane, and the polar coordinates use r and theta to locate a point on a plane
From playlist THE "WHAT IS" PLAYLIST
Selling Real Estate in Hyperbolic Space - Mel Slugbate (Colin Adams) [1996]
slides for this talk: http://www.msri.org/realvideo/ln/msri/1996/conv/adams/1/banner/01.html Conversations between Mathematics Teachers and Mathematics Researchers December 11, 1996 Selling Real Estate in Hyperbolic Space: Investment Opportunities for the 90's" Mel Slugbate (Colin Adams)
From playlist Mathematics
22. Rome Redux: The Tetrarchic Renaissance
Roman Architecture (HSAR 252) Professor Kleiner characterizes third-century Rome as an "architectural wasteland" due to the rapid change of emperors, continuous civil war, and a crumbling economy. There was no time to build and the only major architectural commission was a new defensive
From playlist Roman Architecture with Diana E. E. Kleiner
The smartest students solved this by thinking of pizza
The Putnam Exam has legendary difficulty: the average (median) score is usually 1 out of a possible 120 points. No calculators allowed though, and you have to prove everything very carefully. This geometry problem appeared on one of the tests, and there is a neat way to solve it! Thanks
From playlist Math Puzzles, Riddles And Brain Teasers
18. Hometown Boy: Honoring an Emperor's Roots in Roman North Africa
Roman Architecture (HSAR 252) Professor Kleiner discusses two Roman cities in North Africa: Timgad and Leptis Magna. Timgad was created as an entirely new colony for Roman army veterans by Trajan in A.D. 100, and designed all at once as an ideal castrum plan. Leptis Magna, conversely, g
From playlist Roman Architecture with Diana E. E. Kleiner
Determine the values of two angles that lie on a lie with a third angle
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure