Could any one tell me what are the fundamental contrasts with postulates of Euclidean Geometry and Spherical Geometry? I myself see these things, please tell me if there are more: Lines in EG are great Circles in SG, we can extend infinitely a line in EG but there is no great circle in a sphere which has arbitrary radius. How do we approach such an amazing work of art? In this section I will attempt to give you a basic road map towards. The ellipse calculator, formulas, solved example & step by step calculations may useful for users to understand how the input values are being used in such calculations. Mathispower4u. They all have a flat surface on one side that tapers to a point on the other side. After reading at some sites I got to know it's something I already knew but just didn't know it by its name. 06 Spherical Capacitor. Skip to content. We can generalize the partial derivatives to calculate the slope in any direction. 5 cm, 3 cm, 7 cm •2 sides and the included angle (SAS) eg. We end with an alternative proof of Euler’s Formula using spherical geometry. The reason that Euclid was so influential is that his work is more than just an explanation of geometry or even of mathematics. 1 A-ne Spaces Geometrically, curves and surfaces are usually considered to be sets of points with some special properties, living in a space consisting of \points. There are about 3,200 tutorials, covering the whole range of second-level mathematics. We will also see how these techniques can be used to solve important problems in the real world. Khan Academy - Supplies a free online collection of thousands of micro lectures via YouTube on numerous topics. All of the videos are closed captioned and ADA compliant. Monday, April 27. The definition of a sphere is "every point that is the same distance from a single point called the center. Sep 07, 2017 · So, honestly speaking I didn't know what is plane trigonometry. Note: Students may not receive credit for Math 2000 and Math 2134 or Math 2231 or Math 2232. Math Analysis Chapter 12 Review Sheet Answers. Spherical geometry is defined as the study of figures on the surface of a sphere, and it can be viewed as the three-dimensional version of Euclidean or planar geometry. Let us consider a surface integral where is a surface which have a parameterization described in terms of angles and in spherical coordinates. welcome to the geometry worksheets page at math-drills. However, it differs from typical Euclidean geometry in several substantial ways: ① There are no parallel lines in spherical geometry. Prerequisite: A grade of "C" or better in MATH 096, recommending score on the placement test, or consent of the mathematics department. Mathispower4u. Much of the knowledge of these peoples was well-known around the Mediterranean, and when the Greek civilisation began to assert itself in the 4th century BCE, philosophers like Aristotle (384-322 BCE), developed a particular way of thinking, and promoted a mode of discussion which required the participants to state as clearly as possible the basis of their argument. Derivation of Formula for Total Surface Area of the Sphere by Integration The total surface area of the sphere is four times the area of great circle. 05:28 History of the 4th of July: Crash Course US History Special. The figure above represents a monohybrid cross of F1-hybrid plants. (11037 views) Plane and Spherical Trigonometry by Elmer A. With the inclusion of spherical geometry, mathematicians now had three broad types of geometry with which to study and measure shapes and space: hyperbolic (Lobachevsky), spherical (Riemann), and flat (Euclid). I used spherical trigonometry to calculate all the angles for the 48 and the 120 LCD spherical triangles of the vector equilibrium and the icosahedron generated by the primary great circles. Both parent plants are heterozygous (Ss) for an allele that determines seed shape. Semi-automatically filtered from a common source file. Use this quick reference to find definitions of common GD&T symbols and terms. Online Library Holt Geometry 11 7 Practice C Answers This video provides a little background information and three examples of how to find the center and radius of a circle, given an. No matter how you position the three sides of the triangle, the total degrees of all interior angles (the three angles inside the triangle) is. I'm doing first year Computer Science now, however I'm not sure if they'll teach me what is required and also I'd like to get to it more quickly, so I'm asking - what is the fastest way to learn Spherical Harmonics?Assuming my high school math was solid, where do I start from?I've used them before, however I just used ready algorithms. Simon built a Polar to Cartesian converter (Simon's own code). The gradient vector <8x,2y> is plotted at the 3 points (sqrt(1. Although closely related, the two ideas of spherical and planar geometry are completely different. David Eppstein, Theory Group, ICS, UC Irvine. Click below to download the free player from the Macromedia site. The first step in taking a directional derivative, is to specify the direction. Geometry and Trigonometry in Menelau's theorem (100 dC) Summary: History can be useful for science teaching. Parallel lines are in the same plane and do not touch, even when extended out to infinity. area, center of mass, moments of inertia. I'm on board with this. To summarize: it's difficult to imagine any area of math that is more widely used than geometry. solar system calculator - by don cross - cosine kitty. you need Math. This site contains definitions, explanations and examples for elementary and advanced math topics. Intro to Spherical Trig. Math · Multivariable calculus · Integrating multivariable functions · Triple integrals (articles) Triple integrals in spherical coordinates How to perform a triple integral when your function and bounds are expressed in spherical coordinates. 2 method of composite areas example 6, page 4 of 5 y x 4 in. 24 Triple Integrals in Cylindrical and Spherical Coordinates lecture video (13. 12 [Paid] APK Free Download Latest version for Android. ), carry out transformations on these objects (dilations, re. Extended research regarding how spherical geometry could be used has been presented in a sophisticated, and clear manner. In the spherical geometry the interior angles always add up to more than two right angles (180 degrees), in the planar geometry they add up to exactly two right angles, while in the hyperbolic geometry they add up to less than two right angles. calculate the scaled planet diameters and planet-sun distances for a solar system model. In real life, there are many different applications of geometry including everyday uses such as the "stop sign," which is an octagon shape. This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas. I think they usually get the gist of what we're doing, but they usually struggle with the GREATEST part of GCF. My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. Looking at words this way will help their meaning and usage stick in your mind. The Khan Academy in the math classroom. 7-8 Cylindrical and Spherical Coordinates; (Khan Academy) Intro to Line Integrals. Web Study Guide for Vector Calculus This is the general table of contents for the vector calculus related pages. Each chapter has 4 sections. Welcome to Math Insight. The goal today is to make sure students get exposure to the typical variety of scientific notation word problems. As the plot shows, the gradient vector at (x,y) is normal to the level curve through (x,y). Just "plug and chug," as they say. The Internet's premier ask-an-expert math help service. December "How mathematicians rule the markets" "How to fix Math Education" Beyond the spherical cow May 2001. Practice the relationship between points, lines, and planes. This can very easily be extended to equating areas of the spherical cap, by slicing the spherical cap into multiple small slices and adding each one's area. the Math Tutoring Center for no cost (see "Tutoring and Extra Help" below). thousands of free educational videos. We've all seen a hexaflexagon folded out of paper, but how about a burrito? Vi Hart, a "mathmusician" over at the Khan Academy, came up with the Flex Mex, a burrito folded into a hexaflexagon with all the toppings inside. 2 Vectors in 3 Dimensional Space 11. Khan Academy. But please read why first: To pinpoint where we are on a map or graph there are two main systems: Cartesian Coordinates. From the Legendre polynomials can be generated another important class of functions for physical problems, the associated Legendre functions. Sep 20, 2012 · This week, That's Maths (TM005) discusses the large range of maths education videos that are available free of charge from the Khan Academy website. With the linearity property, Laplace transform can also be called the linear operator. The ellipse calculator, formulas, solved example & step by step calculations may useful for users to understand how the input values are being used in such calculations. A key concept in coordinate geometry is analyzing graphs to determine distances and areas that depend on the scale and units of measure. z x y= +2 2 2. Students can watch the video anywhere, anytime, all the time and NEVER be concerned about. ) Homework Due Date. There will not be a quiz this Wednesday. If all you are interested in is where you stand compared to the rest of the herd, you need a statistic that reports relative standing, and that statistic is called a percentile. Of course the Khan Academy has very easy-to-understand lectures, but not in all of the above mentioned topics. Skip to main content. There are separate table of contents pages for Math 254 and Math 255. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric. solid-geometry-calculator. the best selection of free reading comprehensions, language arts, math, social studies, and science teaching materials. Read more Triple Integrals in Spherical Coordinates. Kolecki National Aeronautics and Space Administration Glenn Research Center Cleveland, Ohio 44135 Tensor analysis is the type of subject that can make even the best of students shudder. moments of inertia - university of illinois. We can say that each slice on the sphere will have area equal to the slice on the cylinder, hence area of the spherical cap becomes $2\pi rh = \pi(h^2+a^2)$. solar system scale model calculator. Nov 06, 2019 · All in one. Second, we provide links to Khan Academy (KA) videos relevant to the material on that part of the syllabus. To use the application, you need Flash Player 6 or higher. The best discussion of this topic can be found in Henderson & Taimina's book quoted. In several geometries, a triangle has three vertices and three sides, where three angles of a triangle are formed at each vertex by a pair of adjacent sides. In this section, we will discuss single refraction for a circular boundary, where a beam of light passes from one medium into another. After reading at some sites I got to know it's something I already knew but just didn't know it by its name. Rizo has 9 jobs listed on their profile. And who doesn't want that? Physical. Apr 25, 2014 · Earlier, we featured a blog of Coordinate Geometry practice questions. Let us consider a surface integral where is a surface which have a parameterization described in terms of angles and in spherical coordinates. In this and the following courses, you will learn about many different tools and techniques in geometry, that were discovered by mathematicians over the course of many centuries. 55 hours of lecture / 55 hours of conference. To prove that the surface area of a sphere of radius r r r is 4 π r 2 4 \pi r^2 4 π r 2, one straightforward method we can use is calculus. We have numbered the videos for quick reference so it's. com/exec/system/1223458702. 1 Vectors in the Plane 11. We can say that each slice on the sphere will have area equal to the slice on the cylinder, hence area of the spherical cap becomes $2\pi rh = \pi(h^2+a^2)$. Welcome to Mathispower4u! This site provides more than 6,000 free mini-lessons and example videos with no ads. geometry: algebra: trigonometry: advanced algebra & pre-calculus : calculus: Noncollinear. Further integration specifically with the Khan Academy Math Program is in progress. Related Topics: More Geometry Lessons In these lessons, we shall be looking at a table of surface area formulas and volume formulas used to calculate the surface area and volume of three-dimensional geometrical shapes: cube, cuboid, prism, solid cylinder, hollow cylinder, cone, pyramid, sphere and hemisphere. If the cutting plane is parallel to the base of the cone (or perpendicular to the axis of the cone), a circle is defined. Research paper which focuses on spherical geometry. Enter the height and either both radiuses or one radius and the wall thickness. Using spherical coordinates, show that the proof of the Divergence Theorem we have given applies to V. This is by design. Introduction to Spherical Geometry. Let's define them. They are a tool for adding up infinitely many infinitesimal quantities associated with points in a three-dimensional region. Your vector calculus math life will be so much better once you understand flux. One way to specify a direction is with a vector $\vc{u}=(u_1,u_2)$ that points in the direction in which we want to compute the slope. Feb 02, 2009 · About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the. Naturally, I googled. Discrete Math Exponents Geometry Euclidean/plane conic sections/ circles constructions coordinate plane triangles/polygons higher-dimensional polyhedra non-Euclidean Imaginary/Complex Numbers Logic/Set Theory Number Theory Physics Probability Statistics Trigonometry: Browse College Geometry. In geometry we are concerned with the nature of these shapes, how we. Publications; People; Projects; Opportunities; Blog; Search. Brilliant guides you through problem solving strategies and challenges you to think outside the box. I attempted to take this class in college and could not find the resources I needed online and was forced to drop the class because I could not keep up with the pace of the c. Word Study is meant to help your learning of vocabulary. There will not be a quiz this Wednesday. In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °, π radians, two right angles, or a half-turn. Mad Minute Math HD – This app provides different calculators, including standard, scientific, prime number, square root, properties of a circle, sine, cosine, and tangent. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. See examples below. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the. This lesson provides a comprehensive list of surface area formula of some basic geometry figures such as the cube, the cylinder, the pyramid,. calculate the scaled planet diameters and planet-sun distances for a solar system model. the angles of incidence and reflection are measured from the. Posts about Spherical Geometry written by antwerpenhomeschooling. in Achieving Educational Equity, Popular; STEM Teacher Preparation and Development; Schema-based instruction, which teaches students to focus on the underlying structure of math word problems, improves learning for students of all levels. What is Finite Math? A very common question math faculty get is about the content of Math 124 Finite Math. solar system scale model calculator. Hogendijk, Isis. Suppose the velocity of a fluid in xyz space is described by the vector field F(x,y,z). ) During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions and developing careful proofs. ) make sense in spherical geometry, but one has to be careful about de ning them. download social dance quizlet free and unlimited. , where Q is the region with , inside the sphere , and Q ∫ xdV x ≥0 x y z2 2 2+ + =16 below the cone. 2 2 2 2 2 2 2 2 2 2 2 0 2 2 x x x y x x x x y x y. Postulate 1: A line contains at least two points. |Sophie Germain 2. in these explorations is Geometry Explorer, a virtual geometry laboratory where one can create geometric objects (like points, circles, polygons, areas, etc. This lesson will describe the 6 main trigonometric functions, use them to solve problems, and give some examples. The answer is going to be quite long and comprehensive, read till the end, its worth it: See, Math is divided into the following 8 parts. In some cases it is advantageous to make a change of variables so that the double integral may be expressed in terms of a single iterated integral. We expect the excess electrons to mutually repel one another, and, thereby, become uniformly distributed over the surface of the shell. Current Location > Math Formulas > Linear Algebra > Definition of Zero Matrix Definition of Zero Matrix A matrix is known as a zero or null matrix if all of its elements are zero. download solar system model online free and unlimited. In this paper we present Me-nelau's theorem in spherical version. Research paper which focuses on spherical geometry. But what we’ll do is we’ll define the triple integral. As the plot shows, the gradient vector at (x,y) is normal to the level curve through (x,y). In Cylindrical coordinate system, a position in a 3D plane is considered in the context of letting a cylinder sit the position of center. All of the videos are closed captioned and ADA compliant. we notice that for any lune of angle a we may consider another lune with the same sides and with angle 360 degrees-a. A spherical triangle is formed by connecting three points on the surface of a sphere with great arcs; these three points do not lie on a great circle of the sphere. As afﬁne geometry is the study of properties invariant under afﬁne bijections, projective geometry is the study of properties invariant under bijective projective maps. Jun 09, 2017 · Yes and no, let me explain. 7 Surfaces 12. This geometry is also called Euclid geometry. If there’s a topic you want to learn about—no matter how basic or advanced—chances are Khan Academy has a video lesson for it. 7-8 Cylindrical and Spherical Coordinates;. Kelly MacArthur. Cartesian coordinates allow one to specify the location of a point in the plane, or in three-dimensional space. They are a tool for adding up infinitely many infinitesimal quantities associated with points in a three-dimensional region. Vectors and the Geometry of Space 11. To know more about great circle, see properties of a sphere. The result resembled the supershapes Simon had programmed with Paul Bourke’s formulas before. SpringBoard. 6 Lines, Curves, and Planes 11. Homework problems are NOT collected or graded. com/exec/system/1223458702. David Eppstein, Theory Group, ICS, UC Irvine. This property can be easily extended to more than two functions as shown from the above proof. khan academy. Mountain View-based online education company Khan Academy is hoping to Khan Academy to offer free, online SAT prep Advanced), Trigonometry, Euclidean Geometry, Spacial/Spherical Geometry. com/exec/system/1223458702. Online calculators and formulas for a surface area and other geometry problems. geometry: algebra: trigonometry: advanced algebra & pre-calculus : calculus: Noncollinear. 2014 Geometry Khan Academy Video Correlations By SpringBoard Activity Unit 5: Extending Two Dimensions to Three Dimensions Activity 30 Deriving Area Formulas 30-1 Learning Targets: Solve problems using the areas of rectangles, parallelograms, and composite figures. Mar 24, 2015 · Khan Academy: PreAlgebra – Khan Academy Algebra allows students to learn Algebra through different videos. Similarly, positive spherical is called overcorrected and is generally associated with diverging elements. Hi Andy, I am truly glad to hear how Khan Academy has helped you I voted your idea up as while I can't guarantee if this content will be added I can say the Khan Academy Support Team looks over postings and feedback with Khan Academy the sky is the limit so this content could be added in future. Solution: Call the volume of the spherical raindrop V and the surface area S. SEMESTER 1 Mastery Course on Khan Academy Topic 1 - Tools of Geometry. Who Created this Wonderful Form of Geometry? Comparison of Angle Measures Comparison of Perpendicular Lines In spherical geometry angles are defined between great circles. Conic sections are obtained by passing a cutting plane to a right circular cone. moments of inertia - university of illinois. Third, as practice problems are always useful, in addition to the problems available in Stewart and at Khan Academy, we provide practice exams. The rst new geometry we will look at is not actually new at all. Exploration of Spherical Geometry Michael Bolin September 9, 2003 Abstract. essay on dance pdf - oneplus. Math Craft; Here's a great excuse to play with your food—and learn some math while you're at it. Basically, spherical geometry is the 2D geometry described by spherical coordinates but at a fixed radius. Welcome to Math Insight. Many students find the video presentation helpful with learning mathematical material. docx), PDF File (. We define the angle between two curves to be the angle between the tangent lines. Math Analysis Chapter 12 Review Sheet Answers. My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. sphere is extended to form a line, it becomes a great circle (like the equator of the earth). Send email if you know of an appropriate page not listed here. There are several different angles associated with circles. Kelly MacArthur. Hope this helps Proud to be a Khan Academer Katrina. However, if the manifold is equipped with metrics, then the fundamental theorem of Riemannian geometry states that there is a unique Levi-Civita connection, for which the metric tensor is preserved by parallel transport:. moment of inertia of a cylinder about 10. These notes do assume that the reader has a good working knowledge of Calculus I topics including limits, derivatives and integration. And who doesn’t want that? Physical. In this section, we will discuss single refraction for a circular boundary, where a beam of light passes from one medium into another. These fun geometry games for kids offer a great range of free math activities and interactive practice problems that will help kids improve their math skills online. One way to specify a direction is with a vector $\vc{u}=(u_1,u_2)$ that points in the direction in which we want to compute the slope. 12 [Paid] APK Free Download Latest version for Android. Mathispower4u. Harvard College Math 21a: Multivariable Calculus Formula and Theorem Review Tommy MacWilliam, '13 [email protected] It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric. By the 10th century, in the work of Abū al-Wafā' al-Būzjānī, Islamic mathematicians were using all six trigonometric functions, had tabulated their values (Abu al-Wafa had sine tables in 0. If the cutting plane is parallel to the base of the cone (or perpendicular to the axis of the cone), a circle is defined. calculate the scaled planet diameters and planet-sun distances for a solar system model. Posts about trigonometry written by antwerpenhomeschooling. solar system model inputs. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan academy new account keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see which keywords most interested customers on the this website. A triangle in spherical geometry is a polygon with three sides, a quadrilateral is a polygon with four sides, and so on, as in Euclidean geometry. A "related rates'' problem is a problem in which we know one of the rates of change at a given instant—say, $\ds \dot x = dx/dt$—and we want to find the other rate $\ds \dot y = dy/dt$ at that instant. Kolecki National Aeronautics and Space Administration Glenn Research Center Cleveland, Ohio 44135 Tensor analysis is the type of subject that can make even the best of students shudder. Refraction at Spherical Surfaces. Cube Area and Volume. Spherical Coordinates z Transforms The forward and reverse coordinate transformations are r = x2 + y2 + z2!= arctan" x2 + y2,z &= arctan(y,x) x = rsin!cos" y =rsin!sin" z= rcos! where we formally take advantage of the two argument arctan. The ellipse calculator, formulas, solved example & step by step calculations may useful for users to understand how the input values are being used in such calculations. Skip to main content. One tricky part of triple integrals is describing the three-dimensional regions of integration and the resulting bounds on the iterated integrals. This is a cone with a circle for a flat surface that tapers to a point that is 90. solar system scale model calculator. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Hint: evaporation refers to the change of volume over time, so you need to relate volume to surface area to solve this problem. In other instances, test items may not include the graphic. Mathispower4u. com, a free online graphing calculator. An alternative notation for divergence and curl may be easier to memorize than these formulas by themselves. You need previous understanding of how to find an arc length. Related Symbolab blog posts. When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. We define the angle between two curves to be the angle between the tangent lines. Just click on the course to the left. There are about 3,200 tutorials, covering the whole range of second-level mathematics. HMH Fuse: Geometry Sample - This app will allow you a sneak peek at the future of mobile geometry curriculum and includes a free sample chapter. Coordinate Geometry questions for your custom printable tests and worksheets. We are working on the traffic and server issues. math-120 College Math I; math-121 College Math II; 15. Both series' give simple overviews, rather than the deep detail of your textbook. This includes basic triangle trigonometry as well as a few facts not traditionally taught in basic geometry. There is an easy way to remember the formula for the cross product by using the properties of determinants. The classic guide to LaTeX is The Not So Short Introduction by Tobias Oetiker. SEMESTER 1 Mastery Course on Khan Academy Topic 1 - Tools of Geometry. Let S be a surface in xyz space. - Optional Online Course Information. SpringBoard. 2 2 2 2 2 2 2 2 2 2 2 0 2 2 x x x y x x x x y x y. Khan Academy is an education app for everyone—whether you're a parent helping your first grader with geometry or a postgrad looking for a deep dive into microfinance. basic-mathematics. A polygon in spherical geometry is a sequence of points and geodesic segments joining those points. Polking Rice University The material on these pages was the text for part of the Advanced Mathematics course in the High School Teachers Program at the IAS/Park City Mathematics Institute at the Institute for Advanced Study during July of 1996. 2 Non-Euclidean Geometry: non-Euclidean geometry is any geometry that is different from Euclidean geometry. Step by step solution. 7-8 Cylindrical and Spherical Coordinates;. Math 208 Cylindrical and spherical coordinates problems Set up and evaluate problems 1-5 in either cylindrical or spherical coordinates, whichever is more appropriate: 1. Online Library Holt Geometry 11 7 Practice C Answers This video provides a little background information and three examples of how to find the center and radius of a circle, given an. Practice the relationship between points, lines, and planes. How do we approach such an amazing work of art? In this section I will attempt to give you a basic road map towards. Posts about Spherical Geometry written by antwerpenhomeschooling. As the plot shows, the gradient vector at (x,y) is normal to the level curve through (x,y). Download full APK of Math Studio v2. I'm on board with this. ables, line integrals, multiple integrals, spherical and cylindrical polar coordinates. This lecture is part of Fundamentals of Calculus by James Sousa , does not currently have a detailed description. case literature project - Free download as Word Doc (. Kublai Khan is portrayed by Ying Ruocheng in the 1982 miniseries Marco Polo. 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A polygon in spherical geometry is a sequence of points and geodesic segments joining those points. In this section, we will discuss single refraction for a circular boundary, where a beam of light passes from one medium into another. In plane (Euclidean) geometry, the basic concepts are points and (straight) lines. By the 10th century, in the work of Abū al-Wafā' al-Būzjānī, Islamic mathematicians were using all six trigonometric functions, had tabulated their values (Abu al-Wafa had sine tables in 0. txt) or read online for free. Use them as a review of concepts, or when you had to miss a class and need additional help to catch up (come to me for help first!), or explore them for visual intuition into concepts, and just for plain fun:. Recent activity and contributions by Andy Passmore. Nov 14, 2011 · 1. Math24 Menu. The origin is the same for all three. Yet spherical geometry - which is non-Euclidean - does abide by Euclid's fifth postulate. This lesson will describe the 6 main trigonometric functions, use them to solve problems, and give some examples. Mar 24, 2015 · Khan Academy: PreAlgebra – Khan Academy Algebra allows students to learn Algebra through different videos. Many of the pages have closely related free/YouTube videos at the Khan Academy. If the outside surface is polished, is it a convex mirror. Calculus Videos: Krista King, Mario's Math Tutoring, PatrickJMT, MITOpenCourseWare, Khan Academy (Keep in mind that the Khan Academy videos are aimed at a lower level than our class. This is by design.