Definition of Enlargement (Homothetic Transformation: Negative Scale Factor)
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$textbf{Question:}$ It says on Wikipedia that an enlargement of a figure can be described when the scale factor exceeds one. Shouldn't it be when the absolute value of the scale factor exceeds one (i.e. $|lambda|>1$)?
$textbf{Opinion:}$ I also wanted to point out this question has been brought up here as well. The problem I see here is that the definition for $lambda$ is never defined to be new distance over old. It is clear that a figure is getting larger iff $|lambda|>1$ for this situation. I think an enlargement should be defined here to be when $|lambda|>1$ which then implies $|lambda|$ is the ratio of which distances are multiplied. However, that is just my opinion.
geometry analytic-geometry
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
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add a comment |
$begingroup$
$textbf{Question:}$ It says on Wikipedia that an enlargement of a figure can be described when the scale factor exceeds one. Shouldn't it be when the absolute value of the scale factor exceeds one (i.e. $|lambda|>1$)?
$textbf{Opinion:}$ I also wanted to point out this question has been brought up here as well. The problem I see here is that the definition for $lambda$ is never defined to be new distance over old. It is clear that a figure is getting larger iff $|lambda|>1$ for this situation. I think an enlargement should be defined here to be when $|lambda|>1$ which then implies $|lambda|$ is the ratio of which distances are multiplied. However, that is just my opinion.
geometry analytic-geometry
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
$endgroup$
1
$begingroup$
If you read that Wikipedia entry more carefully, you'll se that the scale factor is indeed defined as $|lambda|$.
$endgroup$
– Aretino
Dec 29 '18 at 12:31
add a comment |
$begingroup$
$textbf{Question:}$ It says on Wikipedia that an enlargement of a figure can be described when the scale factor exceeds one. Shouldn't it be when the absolute value of the scale factor exceeds one (i.e. $|lambda|>1$)?
$textbf{Opinion:}$ I also wanted to point out this question has been brought up here as well. The problem I see here is that the definition for $lambda$ is never defined to be new distance over old. It is clear that a figure is getting larger iff $|lambda|>1$ for this situation. I think an enlargement should be defined here to be when $|lambda|>1$ which then implies $|lambda|$ is the ratio of which distances are multiplied. However, that is just my opinion.
geometry analytic-geometry
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
$endgroup$
$textbf{Question:}$ It says on Wikipedia that an enlargement of a figure can be described when the scale factor exceeds one. Shouldn't it be when the absolute value of the scale factor exceeds one (i.e. $|lambda|>1$)?
$textbf{Opinion:}$ I also wanted to point out this question has been brought up here as well. The problem I see here is that the definition for $lambda$ is never defined to be new distance over old. It is clear that a figure is getting larger iff $|lambda|>1$ for this situation. I think an enlargement should be defined here to be when $|lambda|>1$ which then implies $|lambda|$ is the ratio of which distances are multiplied. However, that is just my opinion.
geometry analytic-geometry
geometry analytic-geometry
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
edited Dec 28 '18 at 22:41
W. G.
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
asked Dec 28 '18 at 20:41
W. G.W. G.
7081718
7081718
1
$begingroup$
If you read that Wikipedia entry more carefully, you'll se that the scale factor is indeed defined as $|lambda|$.
$endgroup$
– Aretino
Dec 29 '18 at 12:31
add a comment |
1
$begingroup$
If you read that Wikipedia entry more carefully, you'll se that the scale factor is indeed defined as $|lambda|$.
$endgroup$
– Aretino
Dec 29 '18 at 12:31
1
1
$begingroup$
If you read that Wikipedia entry more carefully, you'll se that the scale factor is indeed defined as $|lambda|$.
$endgroup$
– Aretino
Dec 29 '18 at 12:31
$begingroup$
If you read that Wikipedia entry more carefully, you'll se that the scale factor is indeed defined as $|lambda|$.
$endgroup$
– Aretino
Dec 29 '18 at 12:31
add a comment |
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If you read that Wikipedia entry more carefully, you'll se that the scale factor is indeed defined as $|lambda|$.
$endgroup$
– Aretino
Dec 29 '18 at 12:31