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Sex
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In all wild cattle (loosely defined here as the bison, buffalo and oxen, not the "antelopes" in the same subfamily) and many goats, males and females have horns. Sexual dimorphism is significant: This means the horns of males are generally larger and more robust than those of females (see Reference 1).
Shape
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Wild cattle typically have sharp horns curving upwards not far from the base. The horns of male wild goats are often spectacular, gently arcing scimitars, as in the ibex.
Size
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The horns of male wild goats are typically proportionately larger than those of wild cattle. Those of the markhor may be 60 inches or more for an animal five feet long (see Reference 2). Nonetheless, some cattle have relatively long horns--two feet, for example, in the banteng--and those in the bos family might be massive, especially in water buffalo and gaur.
Pattern
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Ibex, markhor and the wild goat have strongly spiraling or segmented horns. The horns of wild cattle are usually smooth (see Reference 3).
Multiple Pairs
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Most horned ungulates have one pair of horns. Polycerate goats--those genetically coded to grow two or more pairs of horns--are occasionally seen in domestic animals. This trait also exists in some domestic sheep breeds and the four-horned antelope. Goats with as many as eight horns have been recorded (see Resource 2).
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Difference Between Cow & Goat Horns
Goats and cattle both belong to the same family of ungulates (hoofed mammals), Bovidae. Horns are a defining feature of most species in both subfamilies. The underlying anatomy in goat and cattle horns is similar: There is a bony core attached to the skull and sheathed with keratin.