The smoothed octagon is a region in the plane found by Karl Reinhardt in 1934 and conjectured by him to have the lowest maximum packing density of the plane of all centrally symmetric convex shapes. It was also independently discovered by Kurt Mahler in 1947. It is constructed by replacing the corners of a regular octagon with a section of a hyperbola that is tangent to the two sides adjacent to the corner and asymptotic to the sides adjacent to these. (Wikipedia).
Isolating a logarithm and using the power rule to solve
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Condensing mulitple logarithms
👉 Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law
From playlist Condense Logarithms with Brackets
Math tutorial for solving logarithmic equation using inverse operations
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
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
Corinna Ulcigrai - 4/6 Parabolic dynamics and renormalization: an introduction
Parabolic dynamical systems are mathematical models of the many phenomena which display a "slow" form of chaotic evolution, in the sense that nearby trajectories diverge polynomially in time. In contrast with hyperbolic and elliptic dynamical systems, there is no general theory which desc
From playlist Corinna Ulcigrai - Parabolic dynamics and renormalization: an introduction
Corinna Ulcigrai - 1/4 Chaotic Properties of Area Preserving Flows
Flows on surfaces are one of the fundamental examples of dynamical systems, studied since Poincaré; area preserving flows arise from many physical and mathematical examples, such as the Novikov model of electrons in a metal, unfolding of billiards in polygons, pseudo-periodic topology. In
From playlist Corinna Ulcigrai - Chaotic Properties of Area Preserving Flows
Solving a logarithmic equation by using inverse properties
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
How to condense a logarithmic expression using a radical
👉 Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law
From playlist Condense Logarithms with Brackets
C. Judge - Systoles in translation surfaces
I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1). We also determine the ma
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
This German company has been crafting character nutcrackers since 1928! Since how they're made. Stream Full Episodes of How It's Made: https://www.sciencechannel.com/tv-shows/how-its-made/ Subscribe to Science Channel: http://bit.ly/SubscribeScience Like us on Facebook: https://www.fac
From playlist How It's Made
Solving an logarithmic equation
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Condensing logarithms with multiple parentheses
👉 Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law
From playlist Condense Logarithms with Brackets
Solving a logarithm with a fraction
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Laser beams in a maze with octagonal and square cells
Yay, another maze type! This one, suggested in comments, is based on a particular so-called semi-regular tiling, made of regular octagons and squares. The tiling is also called truncated square tiling, or truncated quadrille. At the beginning of the simulation, 15000 laser beams, or parti
From playlist Illumination problem
Yang-Mills, Hodge, and Birch and Swinnerton-Dyer - Million Dollar Equations Part 2 with Tom Crawford
Tom Crawford is back to describe the remaining three million dollar maths problems. Watch the Q&A: https://youtu.be/M4falMG3GIA Watch the first four problems: https://youtu.be/f251NkeDVB8 Subscribe for regular science videos: http://bit.ly/RiSubscRibe The seven million dollar equations ar
From playlist Livestreams
DIY WOODEN PET CAGE indoor K9 dog or cat pen
This pen cost $40 to make and took exactly 3 hours and 7 minutes to complete. The design can be altered to an octagon or to any size. Since it is a one piece non-assembly object, make sure it fits through your doorway. This project requires 10 (2x4) bards 8 feet long, 2 boxes of 2.5" wood
From playlist Best of GreenPowerScience
Alex Wright - Minicourse - Lecture 1
Alex Wright Dynamics, geometry, and the moduli space of Riemann surfaces We will discuss the GL(2,R) action on the Hodge bundle over the moduli space of Riemann surfaces. This is a very friendly action, because it can be explained using the usual action of GL(2,R) on polygons in the plane
From playlist Maryland Analysis and Geometry Atelier
Condensing logarithmic expressions
👉 Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law
From playlist Condense Logarithms with Brackets
Condensing logarithmic expressions
👉 Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law
From playlist Condense Logarithms with Brackets
Topology, Geometry and Life in Three Dimensions - with Caroline Series
If you imagine a three dimensional maze from which there is no escape, how can you map it? Is there a way to describe what all possible mazes look like, and how do mathematicians set about investigating them? Subscribe for regular science videos: http://bit.ly/RiSubscRibe Caroline Series
From playlist Mathematics