Equivalent projection is a term commonly used in cartography and refers to a map projection that preserves areas. The spelling of the word is "ee-kwuh-vuh-lent proh-jek-shun" or /ɪˈkwɪvələnt prəˈdʒɛkʃən/ in IPA phonetic transcription. "Equivalent" is pronounced as "ee-kwuh-vuh-lent" with the stress on the second syllable, and "projection" is pronounced as "proh-jek-shun" with the stress on the second-to-last syllable. This term is important for cartographers as it ensures that the size and shape of objects represented on the map are accurately preserved.
Equivalent projection is a cartographic technique used to represent the Earth's curved surface on a flat surface, such as a map. It aims to accurately preserve shapes and areas of features across the map while distorting distances and angles. In an equivalent projection, each point on the Earth's surface is projected onto a flat surface in a way that the size of objects or areas in the map corresponds to their actual size on the Earth's surface.
Unlike other types of projections that sacrifice accuracy in terms of shape or area, an equivalent projection strives to maintain a proportional relationship between the size of objects and their representation on the map. This means that objects of equal size on the Earth's surface will appear as equal-sized objects on the map.
The most common example of an equivalent projection is the Lambert cylindrical equal-area projection. In this projection, the Earth's surface is projected onto a cylinder that touches the equator and wraps around the sphere. The cylindrical projection accurately represents areas and shapes, but at the expense of significant distortion of distances and directions towards the poles.
Other equivalent projections include the Eckert IV projection, the Mollweide projection, and the Goode's homolosine projection. Each of these projections optimizes the preservation of area while distorting the shape and direction to some extent.
Overall, an equivalent projection provides a compromise between preserving accurate size information while sacrificing accuracy in terms of distances and angles on a flat map.
The word "equivalent" comes from the Latin word "aequivalens", which is the present participle of the verb "aequivalere". This Latin verb is composed of "aequus", meaning "equal", and "valere", meaning "to be strong" or "to be worth". Therefore, "equivalent" implies something that is equal or of the same value as something else.
The term "projection" is derived from the Latin word "projectio", which stems from the verb "proicere". It consists of "pro", meaning "forward" or "forth", and "iacere", meaning "to throw". In this context, "projection" refers to the act of representing a three-dimensional object or space on a flat surface.
When combined, "equivalent projection" refers to a specific type of map projection that accurately preserves the areas of regions on the Earth's surface.