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To specify the ratio between the axes, you can use the aspect_ratio option.
In your first example:
sage: polygon2d([[0.5-0.5,hp/2-qscale*0.05],[0.5+0.5,hp/2-qscale*0.05],[0.5+0.5,hp/2+qscale*0.05],[0.5-0.5,hp/2+qscale*0.05]], fill=False, thickness=1, color='blue',ticks=[None,0.0001], aspect_ratio=500)
In your second example:
sage: for i in [0.1,1,10,100]:
....: show(polygon2d([[0,0],[0,i],[1,i],[1,0]], fill=false), aspect_ratio=1/i)
