4.23. Consider all points on the surface of the Earth for which the geographic latitude equals the longitude. Find the geometric locus of the projections of these points onto the plane of the equator.

## § 5. Area of a Spherical Strip and Volume of a Spherical Segment
4.23. Let's introduce the same coordinate system as in problem 4.22. If the latitude and longitude of point $P$ are $\varphi$, then $P=$ $=\left(R \cos ^{2} \varphi, R \cos \varphi \sin \varphi, R \sin \varphi\right)$. The projection of this point onto the equatorial plane has coordinates $x=R \cos ^{2} \varphi$ and $y=$ $=R \cos \varphi \sin \varphi$. It is easy to verify that $(x-R / 2)^{2}+y^{2}=R^{2} / \mathbf{4}$, i.e., the desired set is a circle of radius $R / 2$ centered at $(R / 2,0)$.