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Around the Solution of a Puzzle

Solve Systems of 2 equations of 2 variables

The Canonical Vector Plane

The Dot Product and the Norm in the Euclidean Plane

Angles in Radians and Trigonometric Functions

The Polar Coordinates and the Rotations

The Complex Numbers as Vectors

The Linear Mappings and their Matrices

Bases in the Plane and Change of Basis

Symmetric, Skew Symmetric and Unit Matrices

Eigenvalues and Eigenvectors

Diagonalisation in the Field of Complex Numbers

Linear Algebra in the Euclidean Plane Section 2 Test

Linear Algebra in the Euclidean Plane Section 3 Test

Linear Algebra in the Euclidean Plane Section 4 Test

Linear Algebra in the Euclidean Plane Section 5 Test

Linear Algebra in the Euclidean Plane Section 6 Test

Linear Algebra in the Euclidean Plane Section 7 Test

Linear Algebra in the Euclidean Plane Section 8 Test

Linear Algebra in the Euclidean Plane Section 9 Test

Linear Algebra in the Euclidean Plane Section 10 Test

Linear Algebra in the Euclidean Plane Section 11 Test

Linear Algebra in the Euclidean Plane Section 12 Test

Linear Algebra in the Euclidean Plane Section 13 Test

Linear Algebra in the Euclidean Plane Final Assessment

First published on Thursday, Jan 9, 2025 and last modified on Thursday, Jan 9, 2025

Linear Algebra in the Euclidian Space: Section 8 test

Fabienne Chaplais Mathedu

Keywords: Complex Number, Polygon

1 Draw an Hexagon and Save the Figure

1.1 Configure Spyder for the figure

Your Spyder doesn’t draw necessarily the figure in an independent window, so that it may be saved on your device.

To do this, go to the ‘preferences’ in the ‘Python’ menu.

Then you select ‘Python Console’ in the left and then ‘Graphics’ upwoards.

Then you check the pop-up menu ‘Backend’ to ‘Automatic’ and you save.

After all of it, you quit Spyder and relaunch it.

1.2 Script to Draw the Hexagon

Here is the script to draw an hexagon.

from numpy import *
	from matplotlib.pyplot import *
	
	#Draw an hexagon
	theta=arange(0,7)*pi/3
	# real numbers from 0 to 6*pi/3=2*pi, by steps of pi\3=2*pi/6
	z=exp(1j*theta)
	x=real(z)
	y=imag(z)
	
	figure()
	plot(x,y)
	xlim(-1.3,1.3)
	ylim(-1,1)
	title(&apos;A regular hexagon&apos;)

Just copy and paste it in Spyder text editor, save it and run it.

Once you have the figure, save it by clicking on the floppy disk at the upper right corner.

2 Question 1: Draw a Pentagon

Adapt the sript to draw a pentagon, with 5 sides instead of 6.

Please copy and paste in your answer the validated script.

Run it and save the figure you obtain, naming it ‘Pentagon.png’.

Copy and paste it in your answer.

3 Question 2: Draw a Circle

To approximate a circle, dapt the sript to draw a polygon with 50 sides, to draw a pentagon.

Please copy and paste in your answer the validated script.

Run it and save the figure you obtain, naming it ‘Circle.png’.