I recently re-drew it from memory for my son, which got me thinking about the original drawings I did of them. I went and found some of them. So I settled for paper and pencil, but not just any would do: I used 1-mm graph paper and a mechanical pencil. With those simple tools, I made some pretty intricate drawings. I would get into almost a trance-like state creating some of them. I treasured that graph paper irrationally, to the point that I would try not to waste any of it.
So I have pages crowded with drawings on both sides click to see larger :. My lattice technique was to start with a hatch-work lattice of a certain size, and then poke holes in it to change the shape of the pieces.
The esthetics of the exercise were to get the holes so that the weave was dense, but not repetitive. I was always fascinated to see how moving a hole would drastically alter the shapes of the component loops.
How could you get them packed in properly? Also on that piece of graph paper was a lattice-of-lattice experiment. The original artwork was drawn on 1mm graph paper with a mechanical pencil, then scanned at dpi and scaled and filtered with the Gimp. The computer-drawn figures here were created with a Python program using aggdraw and Python Imaging Library , then colored with the Gimp.
Created 28 June When I was a teenager, I loved drawing on graph paper. For example, this is a simple one: I like this lattice because it nearly fills a square, consists entirely of loops, is symmetric, and has a pleasing denseness in the center without being simply a hatch-work. So I have pages crowded with drawings on both sides click to see larger : My lattice technique was to start with a hatch-work lattice of a certain size, and then poke holes in it to change the shape of the pieces.
Recognizing that temperature depends more on latitude and altitude, a subscripted graph shows the direct relation of temperature on these two variables References: Humboldt Baron Pierre Charles Dupin.
Dupin portrait, with his map. Dupin choropleth map of France. Choropleth map with shadings from black to white distribution and intensity of illiteracy in France , the first unclassed choropleth map, and perhaps the first modern statistical map. References: Dupin Faraday diagram of a magnet with lines of force. An increasing number of scientific publications begin to contain graphs and diagrams which describe, but do not analyze, natural phenomena magnetic variation, weather, tides, etc.
Jean Baptiste Joseph Fourier. Fourier portrait. Fourier ogive. Ogive or cumulative frequency curve, inhabitants of Paris by age groupings shows the number of inhabitants of Paris per 10, in who were of a given age or over. Fourier biography. Babbage portrait. Babbage Difference Engine. Mechanical device for calculating mathematical tables the Difference Engine [The beginnings of computing as we know it today.
Benjamin Gompertz. Gompertz portrait. Gompertz curve, derived to describe expected mortality statistics for a population of organisms whose probability of death increases as a function of time Gompertz biography. The Gompertz model. Dupin portrait. Dupin choropleth map of literacy in France.
Dupin cartogram map of France. Choropleth map with shadings from black to white distribution and intensity of illiteracy in France , the first unclassed choropleth map, and perhaps the first modern statistical map Dupin biography. Joseph Nicephore Niepce. Niepce portrait. Niepce photo, Point de vue du Gras.
First successful photograph produced an 8-hour exposure. Catalog of Niepce heliographies. Quetelet portrait. Mortality curves drawn from empirical data for Belgium and France Quetelet biography.
Quetelet web site. Guerry's polar diagrams. Guerry barcharts and polar diagrams. References: Guerry Balbi-Guerry maps. The first comparative choropleth thematic maps, showing crimes against persons and crimes against property in relation to level of instruction by departments in France References: BalbiGuerry Guerry Faraday portrait. Faraday's iron filing diagrammes, the earliest ever made. Graphical analysis of natural phenomena begins to appear on a regular basis in scientific publications, particularly in England.
Faraday biography with portraits. Faraday biography. Armand Joseph Frere de Montizon. Dot map of population of France, John Frederick W. Herschel portrait. Fitting a smoothed curve to a scatterplot, advocacy of graph paper and graphical methods as standard tools of science.
Herschel biography. Herschel images. Guerry's map of crimes against persons in France. Guerry's map of crimes against property in France. Guerry's map of "instruction'' in France. Guerry's map of suicides. The first comprehensive analysis of data on "moral statistics'' crimes, suicide, literacy, etc. Graphical rank lists, with lines showing shifts in rank order between categories rank of types of crime from one age group to the next References: Guerry George Julius Poulett Scrope.
First classed depiction of population density on a world map using three broad classes in a dasymetric map Wikipedia: Scrope biography. Scrope biography. Charles Wheatstone. Charles Wheatstone portrait.
Using the Midpoint Formula When the endpoints of a line segment are known, we can find the point midway between them. This point is known as the midpoint and the formula is known as the midpoint formula. A graphical view of a midpoint is shown in Figure.
Notice that the line segments on either side of the midpoint are congruent. The center of a circle is the center, or midpoint, of its diameter.
Thus, the midpoint formula will yield the center point. Access these online resources for additional instruction and practice with the Cartesian coordinate system. Is it possible for a point plotted in the Cartesian coordinate system to not lie in one of the four quadrants? Answers may vary. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants.
Describe the process for finding the x- intercept and the y -intercept of a graph algebraically. The y -intercept is the point where the graph crosses the y -axis. For each of the following exercises, find the x -intercept and the y -intercept without graphing.
Write the coordinates of each intercept. For each of the following exercises, solve the equation for y in terms of x. For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers.
Find the distance between the two points given using your calculator, and round your answer to the nearest hundredth. For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points. If a point is located on the y -axis, what is the x -coordinate? If a point is located on the x -axis, what is the y -coordinate? For each of the following exercises, plot the three points on the given coordinate plane.
State whether the three points you plotted appear to be collinear on the same line. Name the quadrant in which the following points would be located. If the point is on an axis, name the axis.
For each of the following exercises, construct a table and graph the equation by plotting at least three points. Numeric For each of the following exercises, find and plot the x- and y -intercepts, and graph the straight line based on those two points.
Find the distance between the two endpoints using the distance formula. Round to three decimal places. Find the coordinates of the midpoint of the line segment connecting the two points. After graphing it, use the 2 nd CALC button and 1:value button, hit enter. You may enter any number for x and it will display the y value for any x value you input.
After graphing it, use the 2 nd CALC button and 2:zero button, hit enter. Hit enter. Use this to find the x -intercept. A man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
After finding the two midpoints in the previous exercise, find the distance between the two midpoints to the nearest thousandth. Given the graph of the rectangle shown and the coordinates of its vertices, prove that the diagonals of the rectangle are of equal length. In the previous exercise, find the coordinates of the midpoint for each diagonal. Find the distance between the cities to the nearest mile.
A small craft in Lake Ontario sends out a distress signal. A man on the top of a building wants to have a guy wire extend to a point on the ground 20 ft from the building. To the nearest foot, how long will the wire have to be if the building is 50 ft tall? Graph this function on your graphing calculator and find the total cost for one day if we travel 70 mi.
Privacy Policy. Skip to main content. Equations and Inequalities. Search for:. Graph equations by plotting points. Graph equations with a graphing utility. Use the distance formula. Use the midpoint formula. Figure 1. Each section is called a quadrant; the quadrants are numbered counterclockwise as shown in Figure Figure 2.
Figure 3. Figure 4. Analysis Note that when either coordinate is zero, the point must be on an axis. Graphing Equations by Plotting Points We can plot a set of points to represent an equation. Figure 5. How To Given an equation, graph by plotting points. Make a table with one column labeled x , a second column labeled with the equation, and a third column listing the resulting ordered pairs.
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