Height of the pole and the sky at different latitudes

The angle from the horizon up to the north celestial pole is called the height of the pole. It equals the geographic latitude φ of the place: h_P = φ. The proof comes from a diagram in the meridian plane: the plumb line makes angle φ with the plane of the Earth’s equator, the celestial equator lies φ from the zenith, and the pole is 90° from the equator, so the pole stands above the horizon at 90° – (90° – φ) = φ. It follows that the celestial equator at the south point has altitude 90° – φ. So by measuring the Pole Star’s altitude we can find the latitude in the northern hemisphere approximately; Polaris is now ≈ 0.7° from the pole, so the error is under a degree. Uzbekistan lies roughly between 37° and 45° north: Termez ≈ 37°, Samarkand ≈ 40°, Tashkent ≈ 41°, Nukus ≈ 42.5°.