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The difference between a disc (disk) and a circle is crystal clear to me:

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However, in many children's books, a disc is usually called a circle:

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Why do many children's book confuse discs with circles? Should we teach children the difference between a disc and a circle?

Zuriel
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    The underlying reason could probably be the dual meaning of circle in everyday English. Thus, confusion wouldn't be the best word to describe the situation. – Michał Miśkiewicz Mar 25 '22 at 15:41
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    I see an annulus and a disk. – Thierry Mar 25 '22 at 18:00
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    This isn't "confusion", this is (appropriately) using one of the the ordinary English meanings of the word "circle" rather than the technical mathematical definition. – Henry Towsner Mar 25 '22 at 21:36
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    Are you perhaps implying that the surface area of a circle is zero? – knl Mar 25 '22 at 23:18
  • @JoelReyesNoche, you are right. The formula $\pi r^2$ gives the area of a disc, while the area of every circle is zero. – Zuriel Mar 27 '22 at 01:46
  • So, @Zuriel, a ring is a circle, but not a coin? But they you have problems in confusing preschoolers of the important concepts in abstract algebra's definition of a ring. Please keep in mind developmental education, given your "preschool" tag. – amWhy Mar 27 '22 at 22:08
  • I voted to leave this question open, but I suggest to change the title. We can't possibly know why books are this way (or even be sure that the statement is true). We should be rather concerned with the "right" level of detail in education, depending on student age. – Jasper Mar 28 '22 at 10:19
  • @Thierry, how do you draw a circle then? – Zuriel Mar 29 '22 at 14:40
  • In Spanish "círculo" means "disk" and "circunferencia" means "circle". In Johnson's dictionary from the 18th century he defines circle both to mean the curve and the region delimited by the curve, so the dual usage in English has long been common. – Dan Fox Apr 08 '22 at 10:45

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Mathematics, as any other field of inquiry, has specific terminology. The rest of the world is not obliged to use the same technical terminology.

Note that this also happens within mathematics; not every subfield is interested in the same issues and sees the same distinctions as important.

In particular, for young children, the relevant thing to learn is the names of basic figures, together with names of colours, and so on. The minute difference between a circle and a disk is not relevant for a number of years. (Why minute: you have a one-to-one correspondence, so identifying them with each other is quite reasonable for many purposes, even for a professional mathematician. It is usually clear which one we are talking about.)

Tommi
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    Even mathematicians aren't careful about this distinction in many contexts. See the "Gauss circle problem" for example ... https://en.wikipedia.org/wiki/Gauss_circle_problem – David E Speyer Mar 26 '22 at 15:27