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Albert1
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QR Code Length: Examining the Fixed Size of QR Codes
Use the Pythagorean theorem to show that $QR$ is equal to $r\sin\alpha$In summary, the conversation discusses how to prove that the length of $QR$ is fixed, regardless of the position of $P$. It involves using the midpoint $C$ of $OP$, the radius $r$ of the circle, and the angle $\alpha$ between $AOB$. By dropping a perpendicular from $C$ to $QR$, it can be shown that $QR = r\sin\alpha$, which is independent of the position of $P$. The Pythagorean theorem is also mentioned as a helpful hint in proving this.
- #2
Opalg
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MHB
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I assume that $A$, $B$ and $O$ are meant to be fixed, but that $P$ varies, and the aim is to show that the length $QR$ is independent of the position of $P$.
[sp]
Let $C$ be the midpoint of $OP$, let $r$ be the radius of the circle, and let $\alpha$ be the angle $AOB$. The circle with centre at $C$ and diameter $OP$ has radius $\frac12r$ and passes through $Q$ and $R$ (because of the right angles). The angle $QCR$ is $2\alpha$. By dropping a perpendicular from $C$ to $QR$, you see that $QR = 2CR\sin\alpha = r\sin\alpha.$ That depends only on $r$ and $\alpha$ and so is independent of the position of $P$.[/sp]
[sp]
Let $C$ be the midpoint of $OP$, let $r$ be the radius of the circle, and let $\alpha$ be the angle $AOB$. The circle with centre at $C$ and diameter $OP$ has radius $\frac12r$ and passes through $Q$ and $R$ (because of the right angles). The angle $QCR$ is $2\alpha$. By dropping a perpendicular from $C$ to $QR$, you see that $QR = 2CR\sin\alpha = r\sin\alpha.$ That depends only on $r$ and $\alpha$ and so is independent of the position of $P$.[/sp]
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- #3
Albert1
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Re: prove the length of QR is fixed
hint:Albert said:
from the diagram it is clear QR=AC (fixed)
can you figure it out ?
if not I will explain it
View attachment 2606
can you figure it out ?
if not I will explain it
View attachment 2606
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FAQ: QR Code Length: Examining the Fixed Size of QR Codes
What is a QR code?
A QR code is a type of barcode that can be scanned by a smartphone or other electronic device to quickly access information, such as website links, contact information, or product details.
How long is a QR code?
The fixed size of a QR code is determined by the number of data modules, or black and white squares, that make up the code. The most commonly used QR codes are 21x21, 25x25, 29x29, and 33x33 modules in size.
Why is the length of a QR code fixed?
The length of a QR code is fixed to ensure that it can be easily scanned and decoded by various devices. If the code is too small, it may be difficult to scan, and if it is too large, it may not fit on smaller screens or printed materials.
Can the length of a QR code be changed?
Yes, the length of a QR code can be changed by adjusting the number of data modules. However, this could affect the readability and scanning capabilities of the code, so it is important to consider the intended use and compatibility with different devices.
Are there any limitations to the length of a QR code?
Yes, there are limitations to the length of a QR code. The maximum number of data modules for a QR code is 177x177, which can hold up to 4,296 characters of alphanumeric data. However, the more data that is encoded, the denser the code becomes, potentially making it more difficult to scan.