Shape Grapher

The most sophisticated and comprehensive graphing calculator online. Everything You Need to Win. In Graph Theory, there’s a property of graphs called planarity. The first step to create a path is to call the beginPath(). JavaFX Tutorial - JavaFX Line « Previous; Next » In order to render graphics on the JavaFX scene, we need basic shapes and colors. We hope to help you write fantastic graphing lesson plans with just a little extra knowledge. Shape Reveal – Primary Resources. It looks like this: Note that the. Function transformations are math operations that cause the shape of a function's graph to change. Visit Mathway on the web. The official home of the Python Programming Language. Linear-graph definition, graph(def 2b). Problems range in difficulty from average to challenging. An undirected edge between u and v can be given as uv, u<->v, UndirectedEdge [u,v] or TwoWayRule [u,v]. It consists of the grids and the printed lines over it in the shape of squares and the rectangles. Along side of the basic shapes, draw the 3D equivalents, a sphere, cone, and cube. R Package shape: functions for plotting graphical shapes, colors Karline Soetaert Royal Netherlands Institute of Sea Research Yerseke, The Netherlands Abstract This document describes how to use the shape package for plotting graphical shapes. Graph of f(x) = ax 3 + bx 2 + cx + d a > 0 a < 0. 1) reflection across the x-axis x y L G Q 2) reflection. Assume also that g(0) = 4. If the major axis is parallel to the y axis, interchange x and y during the calculation. Count each shape, graph the number, and circle the shape that appears the most often. You will learn how to perform the transformations, and how to map one figure into another using these transformations. 3D Shapes Chart – use the three dimensional shapes chart to teach 9 common 3D shapes to your child. Section 4-6 : The Shape of a Graph, Part II. Welcome to the virtual online graph paper. shape matching algorithm is, the problem of relevant and irrelevant shape differences must be addressed if we want to obtain human-like performance. A semantic graph database technology vendor is supporting a key specification designed to validate graph-based data against a set of conditions that specify the "shape" of data. It looks like this: Note that the. Once this rule has been established, your child can utilize symmetry to divide shapes into equal parts. We then look at more great free online graph makers for Stem and Leaf Plots, Box and Whisker Plots, Histograms, Scatter Plots, Straight Line Graphs, Quadratics, Parabolas, Cubics, and Trigonometry Functions. Honestly you can potentially transform either graph into a different shape. Next, see the graph #262 to use a mask image to get a specific shape!. I’ve also shared a fun game where my kids identified 3-D shapes by touch and an activity that focused my kids on the surfaces that make up various 3-D shapes. 00000001x^2, while quadratic, is VERY close in shape to a line. However, many of the details of a distribution are not revealed in a box plot, and to examine these details one should create a histogram and/or a stem and leaf display. Samurai Graph is a highly functional and user-friendly graph plotter. Math Shape & Weight interactive teaching resources and activities to help your child with Maths. Cannot exceed 1 since ⁡ always lies between -1 and 1. This shape comes from specifications and I am trying to show that the data lie within the bound formed by this shape. BIG IDEAS. Not acceptable graph paper includes pages out of your lab notebook or quad-rule paper (4 squares per inch). Learn exactly what happened in this chapter, scene, or section of Graphing Equations and what it means. Everything You Need to Win. org Calc, but it can also be achieved in non-spreadsheet applications like Adobe Illustrator. We're hoping to bring back a new tool to graph equations, but for the moment, we'd recommend GraphSketch, which is a free tool to produce nice multi-function graphs. Dice_Shape_Graph. If unset, they default to 4, 0. Grapher is a full-featured scientific graphing package, allowing the user to import data in many formats, create and combine a wide variety of 2- and 3-D plot types, and customize the plots in infinite detail. In standard form, a quadratic function is written as y = ax2 + bx + c. Find descriptive alternatives for graph. Graph - Free Graph Plotting Software This freeware draws graphs of mathematical functions in a coordinate system. Make a shape from pieces (circle name) Make a shape from pieces (circle picture) Color the solid figures Draw the missing shape: 2 shapes are missing at the end (LARGER shapes) Draw the missing shape: 1 shape is missing anywhere in the pattern (LARGER shapes) Draw the missing shape: 2 shapes are missing at the end (smaller shapes). It is often useful or necessary to find out what the gradient of a graph is. What exactly does that mean? Well for one thing, it means if there is a point (a, b) on the graph of , we know that the point (a, - b) is located on the graph of. The graph of a function of two variables, f(x, y), is the set of all points (x, y, z) such that z = f(x, y). On your computer, open a drawing in Google Drive. The concept of the distribution was introduced at the beginning of this module. After a short while I decided to give shape to the functions I learned about and the result was 3D Graph! click and drag --> Recommended 3D software: 3D Grapher 3D Graph. Why is this? Well, look at the graph above and imagine extending it to the left more, for negative values of ‘x’ below ‘–5’. The goal is a more agile way of analyzing larger volumes of complex, distributed data. Count the shapes and use your data to fill out the graph. It would be amazing if you could draw them all in one fell swoop, but we're guessing you don't have that many hands. The program displays fou. “Map graphs” are ones where the x and y axes correspond to distance: feet, meters, whatever you want. Both Graph J and Graph H represent an object uniformly losing speed. Does the test always work? What should you do if it fails? 2. "The graph is negative" means that the y-values of the graph are negative. After drafting the walls and windows, doors and closets to scale, add dimension lines. The behavior I want is: (A) When the shapes of the input tensors are known (as in graph_A), I want TensorFlow to calculate all of the shapes in the graph at graph creation time (so it can efficiently allocate resources, etc. Set the shape size according to each placemark value Also set the shape color according to a placemark value Graph's title and color scale as GE screen overlays. To the left zooms in, to the right zooms out. There are several functions that appear very frequently and you should know the shapes of their graphs. You can select different variables to customize these graphing worksheets for your needs. An exploration of the shape of a graph Directions: Answer the questions below the graph. They are mostly standard functions written as you might expect. Graph of f(x) = ax 3 + bx 2 + cx + d a > 0 a < 0. They do not show changes over time. Notice the key by the side of the graph which explains the symbols or lines. The graph of is a reflection over the x-axis of the graph of. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. " It would be nice to be able to draw lines between the table points in the Graph Plotter rather than just the points. To graph a rational function, find the asymptotes and intercepts, plot a few points on each side of each vertical asymptote and then sketch the graph. Click on the Graph It button to see its 3D graph (but not end yet). Apply other options you need. Click on the drawing tool in the Drawing toolbar. The Development of Spatial and Geometric Thinking: Co-ordinating Space in Drawings. 3 learning outcomes – click to view Samples: Shapes match. Previously I said that a bar graph would suffice; well the truth is that it is the basis of the filled shape chart (though other charts can be used as well and I'll mention this later in this blog). These graphing puzzles contain over 40 ordered pairs to plot, divided into 3 to 16 different shapes. Play Shape Surveyor online, here. Moved Permanently. Welcome to the virtual online graph paper. graph objects represent undirected graphs, which have direction-less edges connecting the nodes. or wave kernel; thus, it hears the shape of a graph. Plots & Geometry - powered by WebMath. Graph paper. Automatic graph drawing has many important applications in software engineering, database and web design, networking, and in visual interfaces for many other domains. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency. The Shape of a Function The derivative of a function f'(x) tells us how fast f(x) is changing with respect to x and gives us a measure of the steepness of the graph of f. 2D Shape 2D Graph 3D Shape 3D Graph Hyperbola (xa)2 p2 + (y b)2 q2 =1 Hyperboloid of two sheets (xa)2 p2 (y b)2 q2 + (z c)2 r2 =1 You may remember solids of revolution from calculus. I love teaching TWO skills with just ONE activity, don't you?! These shape graphs are a playful way to teach the names and characteristics of the most common 2D shapes while working on graphing at the same time. If you just click-and-release (without moving), then the spot you clicked on will be the new. Welcome to the Halloween Math Worksheets page at Math-Drills. com How many more. It is working fine now with custom shapes. A numerical index of molecular shape has been derived from the graph of the non-hydrogen molecular skeleton. We say that the graph is symmetrical about the y-axis, and. Ellipse equation and graph with center C(x 0, y 0) and major axis parallel to x axis. Origin offers an easy-to-use interface for beginners, combined with the ability to perform advanced customization as you become more familiar with the application. As the degree increases above 1, the graph gets points of inflection where it changes direction. The file generated by GE-Graph can be exported to Google Earth. Line Graph. Classifying Angles Game. It uses a DATA step to add a color variable and a shape variable to the data set, shapes to distinguish iris species, colors to distinguish iris species, and a NOTE statement to simulate a legend. Simple rules for plotting points. To graph a rational function, find the asymptotes and intercepts, plot a few points on each side of each vertical asymptote and then sketch the graph. Note: For more playful ways to learn about shapes, see my teaching shapes to kids page. With the text block selected, type a title. Most of the graphs we do relate to the theme of the day. You can add shapes, such as boxes, circles, and arrows, to your workbooks and presentations. If you guys need I can provide a link to plot each of these graphs. See also Linear Explorer, Cubic Explorer. The geometries of polygon-based shapes are also affected by the node attributes regular, peripheries and orientation. 1 Quiz 05A In each of the following, find a cubic function with the given properties. Graph J has a negative acceleration while Graph H has a positive acceleration. Give them a hexagon and have them build a bigger one and a bigger one and a bigger one You can also do it with trapezoid or the square. " Ghader Yosefi, Iran. Powered by Create your own unique website with customizable templates. "The graph is negative" means that the y-values of the graph are negative. Rates of change and the slope of a curve. Move and modify geometric shapes. Includes all the functions and options you might need. Create online graphs and charts. For each shape plot the ordered pairs on the axis and connect them in order. (Word for the web doesn't support shapes. Transfer the trapezoid to the graph paper. Next, see the graph #262 to use a mask image to get a specific shape!. A summary of Slope in 's Graphing Equations. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. The Shape of a Function The derivative of a function f'(x) tells us how fast f(x) is changing with respect to x and gives us a measure of the steepness of the graph of f. It is working fine now with custom shapes. Scroll the workbook by your finger. For each shape plot the ordered pairs on the axis and connect them in order. Now drop down as many different shapes as it takes to get close to estimating the negative area. Common Graphs. Shapes is a fun educational activity to help children learn basic properties of simple geometric figures. Transfer the trapezoid to the graph paper. Graphing Quadratic Equations. If heat were added at a constant rate to a mass of ice to take it through its phase changes to liquid water and then to steam, the energies required to accomplish the phase changes (called the latent heat of fusion and latent heat of vaporization) would. Rotations of Shapes Date_____ Period____ Graph the image of the figure using the transformation given. A Quadratic Equation in Standard Form (a, b, and c can have any value, except that a can't be 0. Let's consider -x 2-2x+ 3 expression. Click on the images to view, download, or print them. We study the problem of 3D object generation. Graph statements allow for attributes to be set for all components of the graph. Ask your partner to answer your questions. It would be amazing if you could draw them all in one fell swoop, but we're guessing you don't have that many hands. Get started with the video on the right, then check out the example graph from the video as well as challenges below. In our approach, a graph is generated from an over-segmented input image, and a shape matching problem is treated as finding a optimal cycle in the graph. Key Stage 2, Primary/Elementary. Main Menu Math Language Arts Science Social Studies Workbooks Holidays Login Become a Member. And, the second number in the pair is the y-coordinate. When the great potato famine of 1846 struck, many Irish families immigrated to America and brought their Samhain celebrations with them. Since I am very new to Tikz any advice on how I can get started?. Monday, July 22, 2019 " Would be great if we could adjust the graph via grabbing it and placing it where we want too. " It would be nice to be able to draw lines between the table points in the Graph Plotter rather than just the points. the same shape. Like the graphs of quadratics in the plane, their shapes depend on the signs of the various coefficients in their quadratic equations. ColoringCastle. We say that the graph is symmetrical about the y-axis, and. It is the only periodic waveform that has this property. Although there is overlap in how these types of analysis can be employed, we use the term graph algorithms to refer to the latter, more computational analytics and data science uses. The split screen format shows the menus and keystrokes needed to perform or to check. Synonyms for graph at Thesaurus. Start by drawing the three basic shapes, circle, triangle, and square all the same size, freehand, don't be afraid to constantly correct the drawing as needed to perfect the shapes (no rulers). One acceptable type of graph paper is Purdue Form F, available at the bookstores. Example 2: Graph the function. Graph generation is a standard feature in desktop applications like Microsoft Excel or OpenOffice. Does anyone know how to graph a shape like a star or flower using a graphing calculator? YOu can get a flower-like shape by putting it in polar mode and using the. Shape center spread and outliers are used to describe the shape of a dot plot Shape center spread and outliers are used to describe the shape of a dot plot. Test for symmetry: Even and odd functions. The graph of is a reflection over the x-axis of the graph of. Tip: If you want to highlight the data points on your line graph, use the Graph Line and Data Point shapes on Charting Shapes. When you get on Patreon, come back and support graph paper, and music, and all the other wonderful things!!. Step 3: Find the x-intercept(s). To copy a shape, hold Option (on Macs) or Ctrl (on Windows) and drag the copy to a new location. The most sophisticated and comprehensive graphing calculator online. Let’s start with the types of graphs. They do not show changes over time. Graph Visualization. 10x10cm Square glass coaster. Examples of lines, circle, rectangle, and path. We define equivalence classes of shapes and deformations to reduce the dimensionality such that it is practical to search this space for an optimal deformation path between two shapes. Graph Sketcher: Students can create graphs of functions entered as algebraic expressions -- similar to a graphing calculator. Shape Flexer is a bendable shape-able crush-able durable super portable machine washable waterproof extra wind resistant Mega Sun Hat. There are many different kinds of shape matching methods, and the progress in improving the matching rate has been substantial in recent years. The video below is a tutorial on Gradients. I should have done it well since the test code of Stroustrup PPP. ), and (B) When the shapes of the input tensors are unknown (as in graph_B), I want the TensorFlow to wait until runtime. I purchased these cubes in a package labeled for counting in the Target dollar spot this summer. In the previous two sections we’ve looked at lines and planes in three dimensions (or \({\mathbb{R}^3}\)) and while these are used quite heavily at times in a Calculus class there are many other surfaces that are also used fairly regularly and so we need to take a look at those. 2D and 3D Shape Graphing Worksheets This 2D and 3D Shape Graphing Worksheets set is perfect for kids as young as kindergarten. very tall and thin or very squat and fat). Thus, the nodes of the graph represent shape primitives like vectors and quadrilaterals while arcs describing the mutual primitives relations. thus adjusting the coordinates and the equation. Normally used to show how things change over time, a line graph may work better with your project. Graphing Worksheets for Practice. This page will help you to do that. You can graph a Quadratic Equation using the Function Grapher, but to really understand what is going on, you can make the graph yourself. Try to not overlap the shapes since you'll get a more accurate estimate with minimum overlapping. I also cut five of each shape from black poster board. When you let go of the slider it goes back to the middle so you can zoom more. To zoom, use the zoom slider. Trig functions make interesting graphs. Lost a graph? Click here to email you a list of your saved graphs. Use on an IWB, PC or Mac. Flowers and Other Vegetation Roses, tulips, flowers, trees, leaves, fruit and vegetables. Aligned with Common Core State Standards: 5. The behavior I want is: (A) When the shapes of the input tensors are known (as in graph_A), I want TensorFlow to calculate all of the shapes in the graph at graph creation time (so it can efficiently allocate resources, etc. Drawing lines, arrows, and other shapes on a graph. 0 ≤ t ≤ 2π. This printable graph paper (also known as grid paper) features squares of various sizes, from 1 line per inch to 24 lines per inch. In the internet, I have seen users posting graphs of different shapes like a heart-shaped graph and a Batman logo-shaped graph. In TensorFlow, all the operations are conducted inside a graph. Graph Individual (x,y) Points - powered by WebMath. We have since covered the concepts of central tendency and variability as well as frequency charts and graphs. Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. As a calculus student I was fascinated by the shapes of 3d functions. Ask your partner to answer your questions. Try out our rich gallery of interactive charts and data tools. Coordinate pictures are a way of helping to reinforce plotting skills with a game of connect-the-dots. ), and (B) When the shapes of the input tensors are unknown (as in graph_B), I want the TensorFlow to wait until runtime. To graph a rational function, find the asymptotes and intercepts, plot a few points on each side of each vertical asymptote and then sketch the graph. Nerdy Details: The formula you supply calculates the height z from the variables x and y between -1 and 1. Hi I am trying to draw a shape which is very much like a trapeziod on a graph. Numerically solve and graphically display tangent lines and integrals. We must think about whether the sizes, shapes and colors of graphics are helping to make information more clear and helping to increase understanding. What is graph-tool?. Download free on Google Play. For discussing the shape of the graphs, let us discuss some more functions which are not polynomial functions. You can rotate a shape once you make it in either of two ways: click on the shape & if you have a green dot you can just drag it around until you like it’s placement. Rotate the entire piece of patty paper 90° counterclockwise about the origin. Damien Henning is raising funds for Shape Flexer Sunhat LITE! on Kickstarter! A light weight version of the Shape Flexer: a bendable shapeable crushable portable machine washable waterproof wind resistant Sun Hat. I’ve also shared a fun game where my kids identified 3-D shapes by touch and an activity that focused my kids on the surfaces that make up various 3-D shapes. · TLW construct a bar graph using 1” shapes glued to graph paper squares. Nickel Round, Heart & Rectangle shape keyrings. Count each shape, graph the number, and circle the shape that appears the most often. 0, respectively. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. To add a title to the graph, from Charting Shapes, drag a Text block shape onto the drawing page. On what intervals are the function values (y‐coordinates) decreasing? 2. 2D Shape 2D Graph 3D Shape 3D Graph Hyperbola (xa)2 p2 + (y b)2 q2 =1 Hyperboloid of two sheets (xa)2 p2 (y b)2 q2 + (z c)2 r2 =1 You may remember solids of revolution from calculus. Like the graphs of quadratics in the plane, their shapes depend on the signs of the various coefficients in their quadratic equations. But presumably doing such drawing would require having a graphics program of some sort, and if you had that, you wouldn't need the graph paper lines, because the graphics program can display a background grid. Example 2: Graph the function. With a few clicks, you could show your data in a vivid way. To see another way in which the derivative appears, let's go back to our earlier discussion about making measurements. Comparing the flat plate and the prism, and the sphere and the bullet, we see that the downstream shape can be modified to reduce drag. " Ghader Yosefi, Iran. The drag coefficient for a sphere is given with a range of values because the drag on a sphere is highly dependent on Reynolds number. If you want to draw several objects, hold Shift while selecting the drawing tool. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. The preferred analysis and graphing solution purpose-built for scientific research. On this page, you will find Halloween math worksheets on a variety of topics including Halloween multiplication, division, addition and subtraction. Describing the Shape of Distributions. All the geometry help you need right here, all free. Select a size from the dropdown menu. This page contains sites relating to Graphing of Data. Explain how to use the second derivative test to identify and classify local extrema of a twice di eren-tiable function f(x). In this post I'm sharing a 3-D shapes graphing game we played that reinforced the names of six different 3-D shapes while also working on basic graphing skills. Nerdy Details: The formula you supply calculates the height z from the variables x and y between -1 and 1. Mind map A mind map is used to show the different ideas associated with a particular concept. The commonly used graphs for data presentation are: Pictographs - This is the most basic form of graphing. Kids are asked to count the number of each shape in the box and then color in the bar chart to show the correct number of shapes in the graph. Thanks Gaudenz. I have to draw the graph of the function y = 3x^2. This one page worksheet is on plotting ordered pairs. Color the shapes, count, and complete the graph. Rates of change and the slope of a curve. In topology, a subject in mathematics, a graph is a topological space which arises from a usual graph = (,) by replacing vertices by points and each edge = ∈ by a copy of the unit interval [,] where is identified with the point associated to and with the point associated to. You can also toggle between 3D Grapher mode and Contour mode. image/svg+xml. To validate a data graph against the shapes graph, a SHACL processor requires the shapes graph and the data graph as arguments for the validation process. A risk graph is a two-dimensional graphical representation that displays the profit or loss of an option at various prices. 3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. This reveals the true graph of `f'(x)`, drawn in red. It includes a bunch of fun worksheets and a song to keep young mathematicians engaged. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. shape matching algorithm is, the problem of relevant and irrelevant shape differences must be addressed if we want to obtain human-like performance. When you're graphing (or looking at a graph of) polynomials, it can help to already have an idea of what basic polynomial shapes look like. In directed graphs, the connections between nodes have a direction, and are called arcs; in undirected graphs, the connections have no direction and are called edges. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. Click on the images to view, download, or print them. Mathspace has really aided growth throughout my class. An undirected edge between u and v can be given as uv, u<->v, UndirectedEdge [u,v] or TwoWayRule [u,v]. This will create the bottom half of your shape with fill up to the X Axis (light red in the sample). Students must use the grid and coordinates of different shapes to move them and plot new coordinates. I use the floor graph a lot. One row of blocks in the pattern grid will be equal to one row of knitting, and each coloured block represents one stitch. 2D Shape 2D Graph 3D Shape 3D Graph Hyperbola (xa)2 p2 + (y b)2 q2 =1 Hyperboloid of two sheets (xa)2 p2 (y b)2 q2 + (z c)2 r2 =1 You may remember solids of revolution from calculus. Click below to download the free player from the Macromedia site. Graphviz is open source graph visualization software. In particular that the shape made by rotation around the x-axis can stand on the top, if it is made from wood. Algebraic functions are functions which can be expressed using arithmetic operations and whose values are either rational or a root of a rational number. To see another way in which the derivative appears, let's go back to our earlier discussion about making measurements. Solid Shapes Worksheets : 3D Shapes This page contains printable geometry worksheets for teaching solid shapes. Suppose you have data for a collection of securities (like the S & P 500 stocks, for example), and you graph the return rates and standard deviations for these securities, and for all portfolios you can get by allocating among them. The heart curve is a closed curve, which has the shape of a heart. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Shape Graph Materials: container of triangle, square and hexagon pattern blocks, graph template _____ 1. Represent and interpret data. You can also toggle between 3D Grapher mode and Contour mode. The Wikipedia page on planar graphs is filled with awesome facts. The software is designed for middle and secondary math classrooms, but many of its tools are ideal for primary math. graph objects represent undirected graphs, which have direction-less edges connecting the nodes. This tutorial is dedicated to visualisation of graphs and the addition and animation of data on graph renderings. The old equation grapher we provided used Flash, which is grossly out-of-date and not widely supported any longer. Email this graph HTML Text To: You will be emailed a link to your saved graph project where you can make changes and print. A barplot is used to display the relationship between a numeric and a categorical variable. Donnayoung. If I have other details such as approximate square size, that will be made known to you but please keep in mind that your printed results might not be exactly the same. There are all kinds of charts and graphs, some are easy to understand while others can be pretty tricky. You can still draw the dots one at a time. ©K-5MathTeachingResources. ELABORATION · What is the purpose of this bar graph? It shows us a picture of the amount of shapes in our room. A transitive verb is a verb that requires a direct object (e. VBA to manipulate shapes embedded within charts in PowerPoint Hi, If I add a chart to my slide, then with the chart selected insert a shape, that shape is now "part of" the chart (it can not be dragged out of the chart area). Free graphing calculator instantly graphs your math problems. To rotate a shape 90 degrees around the point of origin, turn the x and y coordinates into -y and +x coordinates. Sometimes, we may need to save or export the Excel charts, graphs, shapes or pictures in the workbook as JPEG or PNG image files. Given a shape template and a graph generated from the. Count the shapes and use your data to fill out the graph. Definition of Graph. Math Shape & Weight interactive teaching resources and activities to help your child with Maths. From Charting Shapes, drag the Line graph shape onto the drawing page, and then select the number of data points you want. 2D and 3D Shape Graphing Worksheets This 2D and 3D Shape Graphing Worksheets set is perfect for kids as young as kindergarten. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under  Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: