There is a very, very full and wonderful essay on this topic (in English, translated from the Ruusian original) which can be found here, but I will quote two paragraphs which will significantly add to what has been discussed here already:
It appears to me that the correction קו/קוה (qava/qav) has not merely numerical meaning. The word קוה (qava) is feminine (in Hebrew the feminine words almost always end with ה) while קו (qav) is masculine. The way the word is spelled is called "masoret"-מסורת and is feminine, the way it is pronounced is called "mickra"- מקרא and is masculine. On the other side, in the pair circle-diameter, the circle represents a feminine, material notion (e.g. the mother Earth) while the straight line represents the masculine, spiritual notion (e.g. the rain that fertilizes the earth). Hence the word קוה (qava) is related to the circle while קו (qav) to the diameter. With this correspondence the verse 7:23 reads "קו (qav) ten cubits from the one brim to the other … and a קוה (qava) of thirty cubits did circle it round about". Thus the ratio of a circle to diameter becomes (30xqava)/(10xqav)=333/106.
Notice that that all objects in the tabernacle where straight. May be this is the reason why Rambam draw the Menorah with straight branches? If in the "heavens", in the spiritual world, there are no curved lines, the circle is perhaps represented there by a polygon. In case of the perimeter of the circle, the hexagon could serve as a model. In case of the area, the dodecagon could be the model. In the first case the perimeter is equal 2∙3∙radius of the surrounding circle; in the second case the area equals 3∙square of the radius, as if π=3. That is why the Sages considered the equality π=3 not as an acceptable approximation but as a reflection of a certain spiritual truth.
There is a lot more material there and it is well worth a look, especially if you are mathematically inclined.