Second, click New Mind Map to create a blank mind map.
Third, click on the theme and choose the theme style. Click Customize to freely design the theme.
Fourth, click Layout and select Mind Map.
5. Select the center node, and then press Tab to add subordinate nodes. Press Enter to add a sibling node. Press the Delete key to delete the node.
6. Double-click the central node, enter the central keyword, and double-click the secondary node, followed by the secondary node text. Similarly, third-level and fourth-level nodes can be added after the second-level nodes.
Seven, click the text to modify the node color, background, font size, etc. Click a relationship line to add a relationship line. Click the attachment to add pictures, links and comments.
Eight, after the completion of the production of mathematical mind map, click Export to export JPG, PNG pictures and PDF documents.
There are many things to do in the course of graphic translation and rotation on the geometric sketchpad, which can be used for reference.
Course of geometric sketchpad
Chapter 1 Drawing with Tools
The first section starts the geometric sketchpad and introduces the drawing tools.
1. Start the Geometer's Sketchpad: Click the Start button in the lower left corner of the desktop, select all programs |GSP4.05 applications, and then start the Geometer's Sketchpad.
As shown in figure 1, it is a screenshot of opening the geometric sketchpad file.
Figure 1
Is the window of the Geometer's Sketchpad similar to other Windows application windows? There are control menus, max/min and title bar. The left side of the artboard window is the artboard toolbar, and the right side and bottom of the artboard can have scroll bars to make the artboard handle larger graphics.
On the left side of the drawing board is the drawing board toolbox. Move the cursor over the tool and the name of the tool will be displayed immediately. What are they? They are arrow selection tool, point tool, compass tool, ruler tool, text tool and custom drawing tool.
Compared with the general drawing software, do you feel that its tools are a little less? One of the main uses of the geometric sketchpad is to draw geometric figures. When drawing geometric figures, we usually use rulers and compasses, and their cooperation can draw almost all Euclidean geometric figures. Because any Euclidean geometry can be summed up as "point", "line" and "circle" in the end. This idea of kilometer-to-kilometer mapping has aroused the great interest of countless mathematics lovers because of the "three mapping problems" and has a great influence in the history of mathematics. In a sense, the geometric sketchpad drawing is a modern extension of Euclid's geometric "ruler drawing". Because this practice of building all drawings on basic elements is in line with the idea of kilometers in mathematical drawing thinking.
Hold down the edge of the toolbox and drag it to any position in the artboard window. Different positions have different shapes. Just try it. Can you drag it somewhere and the toolbox will become the shape shown in Figure 2?
Figure 2
As the name implies, guess what they do.
This is its main function, and of course there are others.
You can draw points in any blank space or "online" in the drawing area of the drawing board. A "line" can be a line segment, a ray, a circle, a trajectory or a function image.
Isn't it a pity that you can only draw a perfect circle but not an ellipse? (The Geometry Sketchpad can also draw an ellipse. Please refer to Chapter 2. )
Of course, the line ruler tool is used to draw line segments, and it's not just that!
: Tag (that is, descriptive text) or label the object.
If you think the above tools are not enough (for example, you can't draw a square directly), you can define a new tool.
When selecting a drawing tool, just click the tool with the mouse.
Try to draw a graph as shown in Figure 3.
Figure 3
Draw a point: click the point tool, then move the mouse to the drawing board window and click, and a point will appear.
Line drawing: click the ruler tool, then drag the mouse, move the cursor to the sketchpad window, click, then drag the mouse to another position and release the mouse, and a line segment will appear.
Draw a circle: click the compass tool, then drag the mouse, move the cursor to the artboard window, click (determine the center of the circle), hold down the mouse and drag to another position (the distance between the starting point and the ending point is a radius). Release the mouse and a circle will appear.
Draw intersection point: click the arrow tool, then drag the mouse to move the cursor to the intersection point of the line segment and the circle (the cursor changes from horizontal to horizontal, and the status bar displays "Click to construct intersection point"), and the intersection point will appear. As shown in Figure 4:
Figure 4
Only by clicking between line segments (including lines and rays), circles, line segments (including lines and rays) and circles can the intersection be constructed.
Is it easier to use drawing tools than to operate rulers and compasses?
If you are careful, you will find a small triangle in the lower right corner of the arrow tool and the ruler tool. Hold it down with the mouse for about a second and see what happens.
Select the arrow tool to expand, as shown in Figure 5. There are three tools, namely, move, rotate and zoom, and their usage keys are in the next section.
Figure 5
When the ruler tool is unfolded, there are also three tools, as shown in Figure 6, namely: line segment, ray and straight line. We know how to draw line segments. How to draw a ray straight line with it?
Figure 6
Draw light: move the cursor to the ruler tool, hold down the mouse, and don't release the mouse after the ruler tool is expanded. Continue to move the cursor to the ray tool, release the mouse, and the ruler tool will become. Then click the mouse in the drawing area of the sketchpad, hold down the mouse and drag, and then release it at an appropriate position to draw a ray, as shown in Figure 7.
Figure 7
The arrow on the ray is invisible in the geometric drawing board, and it extends to one end indefinitely.
Draw a straight line: Draw a gourd as usual, please draw a straight line, as shown in Figure 8.
Figure 8
(The arrow on the straight line is invisible in the geometric drawing board, and extends to both ends indefinitely. )
You will also find that the line segment, straight line, ray and circle drawn with the geometric sketchpad have two more points respectively. On the one hand, two points are enough to construct them; On the other hand, they can be dragged. For example, click the arrow tool button, move the cursor to the endpoint of the line segment (note that the cursor will become horizontal) and drag the mouse, and the length and direction of the line segment will change; It is precisely because of more "points" that it is possible to be changed.
Move the cursor anywhere between the end points of the line segment (the cursor is horizontal) and drag the mouse to move the line segment. Drag the line, ray point and line separately and try to change them.
Try to draw a circle and see if you can change its size and position.
(Hint: The circle is determined by two points, the point where the mouse is pressed is the center of the circle, and the point where the mouse is released is the point on the circle. Changing either of these two points can change the circle. Drag the center of the circle and the points on the circumference to change the size of the circle, and drag the circumference to move the circle. )
So, you don't think the graphics drawn by the geometric sketchpad are dynamic graphics?
The graphics drawn by the geometric sketchpad are also easy to mark. Might as well compare it with word's drawing.
Click the text tool, the cursor changes from front to hand, and then move the mouse separately. When the cursor moves over the object, it becomes a mouse click and the object displays a label.
Please mark all the objects in Figure 3. It is also easy to remove the label. Just click on each object in the above picture, and the label will be gone. Each geometric object in the geometric sketchpad corresponds to a "label". When you construct geometric objects in the artboard, the system will automatically mark the objects you draw. The text tool is a label switch, which can show and hide the label of each geometric object in the geometric sketchpad.
Draw simple combined graphics with drawing tools.
Let's use the drawing tool to draw some combination graphics. I hope that through the study of examples, you can be familiar with the use of drawing tools and some related skills.
Triangle (1)
First of all, the production result is shown in the figure. Drag the vertices of the triangle to change its shape and size.
This triangle is a dynamic triangle. It can be dragged into a triangle below, as shown in Figure 9.
Figure 9
Second, the main idea is familiar with the use of the "ruler tool" and drag the points in the picture to change the shape.
III. Observation diagram of operation steps 10. You can understand that a triangle is a figure composed of three end-to-end line segments drawn with a ruler tool.
Figure 10
Open the Geometric Sketchpad and create a new drawing.
Click the ruler tool, move the cursor to the drawing area, click and hold down the mouse to drag, draw a line segment, and then release the mouse.
Click the mouse at the same position and hold down the drag to draw another line segment, then release the mouse. (Note the direction of cursor movement)
Click the mouse in the original place, hold down and drag to draw the third line segment. Move the cursor to the starting point, and then release the mouse. (Note that the starting point will change color)
5. Save the file as a triangle. GSP "
Extension: You can also move the cursor to the drawing area, click and release the mouse drag, draw a line segment, and then click the mouse. Click the mouse again and release the drag to draw another line segment, and then click the mouse. Click the mouse in the original position, and release the drag to draw the third line segment. Move the cursor to the starting point and click the mouse.
Example 2 Triangle (2)
1. The lines on the three sides of the triangle are straight lines, rays and line segments. Drag the vertex of a triangle to change its size and shape, as shown in figure 1 1. This graph can be constructed when explaining the outer angle of a triangle.
Figure 1 1
Second, the key points of knowledge points Learn to use line segment tools, straight line tools, ray tools and their switching.
Third, the operation steps
Open the Geometric Sketchpad and create a new drawing.
Select the line drawing tool to move the cursor to the ruler tool, hold down the mouse button, move the cursor to the line drawing tool, and release the mouse, as shown in figure 12.
Figure 12
Draw a straight line to move the mouse to the drawing board, press the mouse button, drag the mouse to the right, and release the mouse button.
Select the light drawing tool, aim the mouse at the line tool, hold down the mouse button and drag it to the light tool to release the mouse, as shown in figure 13.
Figure 13
Draw a ray, aim the mouse at the left point of the defined straight line (please pay attention to the prompt in the lower left corner of the window before pressing the left mouse button), press the mouse button, drag the mouse to the right, and release the mouse button.
Select the line drawing tool, aim the mouse at the line drawing tool, press the mouse button and drag it to the line drawing tool, and release the mouse. As shown in figure 14.
Figure 14
Draw a line segment, aim the mouse at point C in the upper right corner of the defined ray (pay attention to the prompt information in the lower left corner of the window), press the mouse button, drag it to point B at the right end of the defined straight line (pay attention to the prompt), and release the mouse after matching this point.
Save the file as a three-line triangle. GSP "
Example 3: A circle is inscribed with a triangle.
1. The production result is shown in figure 15. If you drag any vertex of the triangle, the shape of the triangle will change, but it will always be inscribed with the circle.
Figure 15
Second, the main idea is to learn to use the line drawing tool to draw line segments on geometric objects
Three. The operation steps are shown in figure 16.
Figure 16
Open the Geometric Sketchpad and create a new drawing.
Draw a circle Click the Compass Tool button, and then drag the mouse to move the cursor to the artboard window. Click and drag the mouse to another location, release the mouse and a circle will appear.
Draw a triangle. Click the ruler tool button and move the cursor to the circle (the circle will turn light blue). Click and hold down the mouse to move to the right, and then release the mouse. Click and hold the mouse in the original position, move it in a circle to the upper left, and release the mouse; Click and hold the mouse in the same position, move it to the lower left of the starting point of the line segment on the circumference, and then release the mouse.
Save the file as a triangle inscribed in a circle. GSP "
Note: when drawing a line segment, the starting point should not coincide with the point on the circumference; When the cursor moves over the circle, the circle turns light blue. Pay attention to the prompt in the status bar.
Try it: draw three circles passing through the same point, and save the file as "three circles with * * * *". Gsp "(I hope you can try it and use it in the future).
Example 4, isosceles triangle (figure 1)
In this way, when the vertices of the triangle are dragged, the shape and size of the triangle will change, but it will always be an isosceles triangle, as shown in figure 17, which is a geometrically invariant law.
Figure 17
The main idea is to construct isosceles by using "the radius of the same circle is equal", as shown in figure 18.
Figure 18
Third, the operation steps
1. Open the Geometric Sketchpad and create a new drawing.
Step 2 draw a circle
3. Draw a triangle. Click the ruler tool button, move the cursor to a point on the circumference (that is, the end point when drawing a circle, at this time the point will turn light blue), click and hold down the mouse to move to the right to release the mouse; Click and hold down the mouse in the original place, move to the center of the circle to the upper left, and release the mouse; Click and hold the mouse in the same position, move to the lower left corner to the starting point, and then release the mouse.
4. Hide the circle and press the "Esc" key (cancel the drawing state). After clicking the circle, press the shortcut key "Ctrl+H" to hide the circle.
5. Save the file as "isosceles triangle 1.gsp"
Perpendicular bisector of line segment
1. The production result is shown in figure 19. No matter how you drag the line segment, the vertical line is the middle vertical line of the horizontal line segment.
Figure 19
The main idea is to learn to use the ruler tool, draw line segments and straight lines, and learn the skills of constructing equal circles, as shown in Figure 20.
Figure 20
operation sequence/order
1. Open the Geometry Sketchpad to create a new drawing and draw a line segment.
2. Draw an equal circle. Click the compass tool, and then drag the mouse to move the cursor to the left end of the sketchpad line segment. Click and drag the mouse to the right end of the line segment, and then release the mouse. Click and hold down the mouse at the same position and drag to the left to the starting point (that is, the starting point of the circle structure) to release the mouse.
3. Draw a straight line Select the straight line tool, move the cursor to the intersection of two circles, click and hold down the mouse to drag to the intersection of the other two circles, and then click and release the mouse. (When the cursor reaches the intersection of two circles, both circles will turn light blue at the same time. )
4. Hide the two circles and the intersection point, and press the "Esc" key to cancel the drawing state. Click the circle and the intersection, and then press "Ctrl+H".
5. Save the file Save the file as "perpendicular bisector". GSP ".
Can you relate the above exercise to the exercise of equilateral triangle?
Extension: drawing of equilateral triangle (1)
Learn the construction method of equal circle, and use "the radius of the same circle is equal" to construct equal sides, as shown in Figure 2 1.
Figure 2 1
Second, the operation steps
1. Open the Geometric Sketchpad and create a new drawing.
2. Draw an equal circle, click the compass tool, then drag the mouse, move the cursor to the sketchpad window, click and hold, drag the mouse to another position, and release the mouse; Click and hold down the mouse at the same position and drag to the left to the starting point (that is, the starting point of the circle structure) to release the mouse.
3. Draw a triangle when drawing a line segment, move the cursor to the intersection of two circles, and click the mouse when the two circles turn light blue at the same time.
4. Hide the two circles and press Esc to cancel the line drawing. After clicking the circle, press "Ctrl+H" to hide the circle.
Save the file as "equilateral triangle 1.gsp"
Example 6. Right triangle (figure 1)
First, the production results drag the left and top points to change the size and shape of the triangle, but it is always a right triangle. Drag the right point and three sides to change the position of the right triangle, as shown in Figure 22.
Figure 22
Second, the main idea is to learn to use light drawing tools; Use the selection tool to draw the intersection; Draw a line segment on the circle; To be clear, the principle of drawing a right angle is that the circumferential angle opposite to the diameter is a right angle.
Third, the operation steps
1. Open the Geometric Sketchpad and create a new drawing.
2. Draw light: Move the cursor to the ruler tool and hold down the mouse. Do not release the mouse after the ruler tool is expanded. Continue to move the cursor to the ray tool, release the mouse, and the ruler tool will become. Then click the mouse in the drawing area of the sketchpad, hold down the mouse and drag it, release it at an appropriate position, and draw a light, as shown in Figure 23.
Figure 23
3. Draw the intersection of circle and ray: move the cursor to the intersection of ray and circle, and click, as shown in Figure 24.
Figure 24
Note: When the cursor reaches the intersection of the ray and the circle, both the ray and the circle will turn light blue, and the prompt in the status prompt bar is "Click to construct the intersection".
4. Draw a right angle, click the ruler tool button, move the cursor to the endpoint of the ray (the endpoint will turn light blue), click and hold down the mouse to move to the circle to the right, and release the mouse; Click and hold down the mouse in the original place and move it to the lower right of the intersection of the circle and the ray, as shown in Figure 25.
Figure 25
5. Hide rays, circles and centers. Click the circle, center and ray continuously, and press the shortcut key "Ctrl+H", as shown in Figure 26.
Figure 26
6. Draw the hypotenuse, click the ruler tool, move the cursor to the left point, click and hold down the mouse, move to the right point, and release the mouse.
Maybe you will say, why is it so complicated? Why not draw a right triangle directly with the ruler tool? However, the right-angled triangle drawn in this way cannot be guaranteed to be a right-angled triangle all the time because it does not define the geometric relationship and drag any vertices and sides.
7. Save the file as a right triangle. GSP "
I wonder if you realize from the above example:
1) When drawing geometric figures with the geometric sketchpad, the first thing to consider is the geometric relationship between objects, rather than the simple accumulation of basic elements (points, lines and circles).
2) Points can be used not only in the blank space of the sketchpad, but also on geometric objects (except "indoor"). The same is true for the starting and ending points of line segments and circles, that is, they can be used not only in the blank space of the drawing board, but also on geometric objects, that is, to construct the geometric relationship between "points" and "lines".
3) Arrow selection tool can be used not only for selection, but also for constructing intersection points.
4) When drawing points (or circles, lines, line segments and rays), move the cursor to the geometric objects (points and lines), and the geometric objects will turn light blue. Click the mouse to make sure that the "point" and "point" coincide and the "point" is on the "line".
5) For drawing auxiliary lines, you can't delete them under normal circumstances, otherwise the related objects will be deleted. Only the shortcut key "Ctrl+H" can be selected to hide.
Section 3: Selecting, Deleting and Dragging Objects
The previous description involves the selection and dragging of objects. Although the Geometer's Sketchpad is a windows software, its object selection method is different from the general windows drawing software. I hope you can realize and pay attention to this during your study. I also hope that through the explanation of this section, you will have a more systematic and comprehensive understanding of this.
First, choose
Before making all selections (or not), you need to click the arrow selection tool button to make the mouse in the arrow selection state.
1. Select one: aim at a point, a line, a circle or other graphic object in the sketchpad with the mouse, and click the mouse to select this object. When a graphic object is selected, it will be emphasized. As shown in the figure below:
Select Object Process _ Description _ Pre-selection Status _ Post-selection Status
Aim at the point to be selected with the mouse. Click the left mouse button when the cursor becomes horizontal.
For straight lines, point the mouse at the part between the end points of the line segment (not the end points of the line segment). Click the left mouse button when the mouse changes to a horizontal black arrow.
A circle is aimed at the circumference (not the center of the circle or the point on the circle) with the mouse. Click the left mouse button when the mouse changes to a horizontal black arrow.
2. Select another object: after selecting one object, click another object with the mouse, and the new object is selected, while the original selected object is still selected (it is not necessary to hold down the "Shift" key when selecting another object, which is different from the selection habit of general windows software).
3. Select multiple objects: click the objects to be selected continuously (note: it is not allowed to click in the blank space of the drawing board when clicking (or press the "Esc" key).
4. Cancel one: after selecting multiple objects, if you want to cancel one, just click the object to cancel the selection.
Unchecked: If you click (or press the "Esc" key) in the blank space of the artboard, all the selected marks will disappear and no objects will be selected.
Select All: If you select the selection tool in the sketchpad toolbox, there will be a "Select All" item in the edit menu; If the current tool is a point drawing tool, this item becomes "All Points"; If it is a line drawing tool or a drawing tool, this item becomes "Select all line segments (rays, lines) or" Select all circles ". Its shortcut key is "Ctrl+A" (please pay attention to and practice this way of selecting similar objects repeatedly).
Select the parent object and child object of the object: after selecting some objects, select Edit | Select Parent Object, as shown in Figure 27, to select the parent object of the selected object. Similarly, sub-objects can also be selected. If an object has no parents, then the geometric sketchpad thinks it is its own parents; Similarly, if an object has no children, it is its own children. The so-called "parents" and "children" refer to the derived relationship between objects. For example, if a line segment is derived from two points, then the "child" of these two points is the line segment and the "parent" of the line segment is the two points.
Figure 27
Note: The last object of the artboard construction is selected. Before selecting an object, it is best to click (or press "Esc" key) in the blank space of the drawing board.
Tip: You can also drag the box to select multiple objects (the same as general windows software), as shown in Figure 28:
Figure 28
If you want to draw quickly, you'd better be familiar with this choice.
The purpose of selecting an object is to manipulate it. This is because in windows, all operations can only act on the selected object, that is, the object must be selected before related operations can be carried out. In the Geometric Sketchpad, you can perform the following operations on the selected objects: delete, drag, construct, measure and transform. Here, we first introduce the delete and drag operations.
Second, delete
Delete is to delete an object (point, line or circle) from the screen. The method is: first select the object to be deleted, and then select the "Clear" item in the "Edit" menu or press the "Delete" key on the keyboard. Please note that all objects related to this object will be deleted at this time, which is different from ordinary windows software and very similar to mathematical thinking. "If the skin doesn't exist, the hair will attach."
Third, drag
You can select one or more objects with the mouse. When you drag the selected objects with the mouse to move in the sketchpad, they will also move with you. Because the geometric objects in the geometric panel are all constructed by geometric definitions, and the essence of the geometric sketchpad is to "keep the geometric relationship unchanged in motion", some related geometric objects will also move with it.
When you drag a graph in the sketchpad, you can feel the dynamic function of the geometric sketchpad. Please note: Before dragging, press the "Esc" key, or click the Select Arrow tool to select the object to be moved.
Try to drag according to the following steps, and pay attention to the change of the graph.
Graphic dragging operation before dragging graphic solution after dragging _ _
1_ gap _ line segment is controlled by point B, so it should follow the movement.
2 drag the direction of line segment AB unchanged, and the position changes. Because point A and point B are the parents of the line segment, they must keep the corresponding relationship, so these two points also move accordingly.
3 drag point B. Point B is the parent point of the circle, so the size of the circle changes with the movement of point B. Because point A is free and not controlled by point B, the position of point A remains unchanged.
4 drag point A is the parent point of the circle, so the size of the circle and the position of the center of the circle change with the movement of point A. Because point B is free and not controlled by point A, the circle always stays in the past of point B. ..
5 A circle is defined by two points AB, and point C is another point on the circle. Drag point C ... Because point C is a child of a circle and is controlled by the circle, it can only move on the circle.
6 draw two intersecting line segments, draw their intersection points with the selection tool (please pay attention to the prompt in the status bar), and then drag the line segment CD. When two line segments do not intersect, the intersection will not be displayed (at this time, the intersection has no mathematical significance).
In the previous study, did you use the circle drawing tool to draw three circles passing through the same point and save them as "three circles with * * * points"? Gsp "file. Now, please bring up this file (choose File | Open command, select the file name, and then press OK). Please select any circle and pull it at will to see if these three circles can still "cross the same point". The result of dragging may be as shown in Figure 29:
Figure 29
Why do graphics "fall apart"? Perhaps the drawing process is like this (the following is the most typical method of "drawing three circles little by little" for beginners, which may be influenced by traditional drawing methods such as drawing on the blackboard or general drawing software), as shown in Figure 30.
Figure 30
In the process of dragging, the geometric sketchpad can keep all the given geometric relations, because it is designed according to geometric relations! So, think about it, what kind of geometric relationship does the above method give when drawing a circle?
As we know, the circle is determined by two points, the point where the mouse is pressed is the center of the circle, and the point where the mouse is released is the point on the circle. Changing either of these two points can change the circle.
In our operation just now, we gave the geometric relationship that each circle is determined by two completely free points (please observe that there are six free points in the figure). According to this geometric relationship, each circle can be changed at will. This shows that in the geometric sketchpad, you can't draw at will like on the blackboard, but you should always consider the geometric relationship.
So how can we ensure that they pass the same point? Why not follow the following steps?
Step by step _ _ Description _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1 Select the circle drawing tool. (None)
Draw the first circle: the center of the circle is a, and a point on the circle is B.
3 draw the second circle; Press the mouse button at any point to specify the center of the circle. C. Drag the mouse to aim at point B (pay attention to the prompt in the status bar), and release the mouse at point B, that is, the point on the circle is B.
Draw the third circle: press the mouse button at any point to specify the center D, drag the mouse, aim at point B (pay attention to the prompt in the status bar), and release the mouse at point B, that is, the point on the circle is B.
Mathematical rotation drawing step 1, rotation A graphic transformation that rotates a graphic by an angle around a certain point o is called rotation. Point o is called the center of rotation, and the rotation angle is called the rotation angle.
2. Rotation has three elements: (1) the center of rotation; (2) direction of rotation; (3) Rotation angle.
3. The nature of rotation: (1) The distance from the corresponding point to the rotation center is equal; (2) The included angle of the connecting line between the corresponding point and the rotation center is equal to the rotation angle; (3) Graphic congruence before and after rotation.
4. Basic steps of rotation drawing: (1) Define rotation center, rotation direction and rotation angle.