Detailed steps for drawing irrational number points using geometric sketchpad

In mathematical geometry, we often need to accurately draw irrational points. The geometric sketchpad software provides a convenient and fast method for users to easily draw these points. Next, PHP editor Zimo will introduce in detail the steps of drawing irrational number points with the geometric sketchpad to help everyone master this practical skill and understand its application in the construction of geometric figures.

Method 1 Geometric method

For example, √2 is the diagonal (hypotenuse) of a right triangle with side length 1, and then use a ruler and compass to draw the drawing on the geometric sketchpad.

Given line segments AB and AC, where t1=1, indicating that the unit is distance. Execute mark distance command on parameters. The length of line segments AB and AC is 1cm. Calculate the square root of the sum of AB2 AC2 and the resulting value is the length of line segment BC. You can verify that the hypotenuse BC is the square root of 2 by measuring the distance between the three sides. Any point on this line segment is an irrational number point.

Method of second algebra calculation

Use the calculation command under the [Data] menu of the geometric sketchpad to obtain the approximate value of the irrational number, and then use the [Calculation command under the [Drawing] menu) Draw Point】 command realizes drawing irrational number points.

If there is such a coordinate point, one coordinate is a rational number and the other is an irrational number. The method of drawing the coordinate point is as follows:

Create a new parameter t1=1, with no unit, and use this parameter as the horizontal coordinate.

Use the calculation command to calculate the approximate value of the irrational number. As the ordinate, the calculated irrational number is as shown in the figure.

Draw irrational coordinate points. Click the [Draw Point] command under the [Draw] menu to open the Draw Point dialog box, click the parameters t1, (1 √17)/2=2.56, and click [Draw] to establish the coordinate point A. Similarly, you can Draw another irrational number point B.

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