2. https://www.cut-the-knot.org/Generalization/div9.shtml
"At this point, be began utilizing" should be
"At this point, we began utilizing"
I also found "iff" a couple of times on this page, but this might be an abbreviation for "if and only if".

3. https://www.cut-the-knot.org/do_you_know/compass.shtml
"The assertion that every ruler-and-compass construction could be accomplished with a ruler" should be
"The assertion that every ruler-and-compass construction could be accomplished with a compass"

Alex

https://www.cut-the-knot.org/pythagoras/midpoints.shtml
"For odd n, the blue circle indicates one of the polygon's vertices. Once you move the cursor into the blue circle"

"blue" (2 times) should be "red" (even though the red circle has 1 blue pixel at the center when problem is solved)

My silly error...

Link https://mathforum.org/epigone/geometry-pre-college/snoxkhawoi/dtiazh10nirm@mathforum.org to "example" is broken.

The new link is https://mathforum.org/epigone/geometry-pre-college/snoxkhawoi/dtiazh10nirm@forum.swarthmore.edu

https://www.cut-the-knot.org/Mset99/math.shtml
"is grotesque not just empty" - comma missing
"those who does it" should be "those who do it"

https://www.cut-the-knot.org/Mset99/together.shtml
"imlementation" should be "implementation"

The link https://www.mssm.edu/ophth/Euler/eitheta/eitheta.html to "The number e and Euler’s formula" is broken and I cannot find any link to replace it.

2. https://www.cut-the-knot.org/Curriculum/Geometry/DynoEllipse.shtml
"commponentwise" should be
"componentwise"

3. https://www.cut-the-knot.org/ctk/Pick.shtml
"llok hard" should be
"look hard"

"the Stern-Brocot tree for which this property comes almost for free" - "for" might be a typo (from?) but it may be the proper way to say it.

4. https://www.cut-the-knot.org/blue/Stern.shtml
"direct discendant" should be
"direct descendant"

"from which it follows that the construction of the tree preserves order" - it appears that the HTML code <center> is not sandwiched off immedialy before this sentence, but it may be on purpose.

5. https://www.cut-the-knot.org/pythagoras/PaperFolding/index.shtml
"fold that maps L₁ onto L2₂" should be
"fold that maps L₁ onto L₂"

Link https://chasm.merrimack.edu/~thull/geoconst.html to "H. Abe (1980)" is broken.
The new link is https://www.merrimack.edu/~thull/omfiles/geoconst.html.
See also https://www.wikipedia.org/wiki/Huzita's_axioms

Link https://chasm.merrimack.edu/~thull/OrigamiMath.shtml to "collection of pages" is broken.
New link is https://kahuna.merrimack.edu/~thull/origamimath.html

Link https://www.origami.vancouver.bc.ca/info/history.html to "Brief History of the Ancient Art of Paperfolding" is broken.
New link is https://www.origami.as/home.html, click "Articles", click "A Brief History of Paperfolding". Since the website is in frames, the web address of the desired article does not show up. Some decoding leads to https://www.origami.as/Info/history.php.

Link https://chasm.merrimack.edu/~thull/geoconst.html to "Humiaki Huzita" (same as the link to "H. Abe (1980)" corrected earlier) is broken.
New link is https://www.merrimack.edu/~thull/omfiles/geoconst.html.

"Therefore, the creases BD₁ and B₁O_D coincide" should be
"Therefore, the creases BD₁ and D₁O_D coincide"

"B₁O_D does pass through the vertex B" should be
"D₁O_D does pass through the vertex B"

"Now, it's all straightforward. Ð B₁BO_B = Ð DB₁B"
Please point out that this is because creases L º DB₁ and AB º O_BB are parallel. I could not see it among all those parallel creases.

In Chapter 3, the author describes a series of experiments where a subject was presented with flushing pairs of digits such as 9 and 7 and had to point out the larger of the two.

'flushing' should be 'flashing'

Errors were in expressions for 28, 30 (2x), 33, 34, 39 (2x), 40, 42, 45 (2x), 46, 48, 66, and 69. These incorrect expressions have been copied to the table at https://www.cut-the-knot.org/arithmetic/funny/4_3.shtml . Incorrect expressions for the above 12 numbers (some with more than one incorrect expressions) are in red (please note that number 72 has all expressions correct, but one expression will be transfered from number 48):

28    33+3/3 = {3·3/.3-Ö3} = 33 + 3/3 = ((3!)!! + (3!)!!)/3 - 3
30    3·3·3+3 = 3!·3! - 3 - 3 = 33 + 3! - 3 = 3·3·3 + 3 = (3·(3!)!! - 3!)/3 = (3!)3/3 - 3!
33    33-3+3 = 33/3·3 = 33 + 3 + 3 = 3!·3! - 3! + 3 = (3!)3!/3 - 3 = 3·Ö(3·(3!)!!) - 3 = ((3!)!! + (3!)!! + 3)/3 = (3!)3/3 - 3
34    33+3/3 = 3!·3! - 3!/3 = (3·(3!)!! + 3!)/3
39    33 + 3 + 3 = 3!·3! + 3! - 3 = (3!)!! - 33!/3 = (3!)3!/3 + 3 = 3·Ö(3·(3!)!!) + 3 = (3! + 3!)·3 - 3 = (3!)3/3 + 3
40    (3 + 3!/3)/3 = (3!)!! - 3! - 3!/3 = (3!)!! - (3!/3)3 = 3!/3·3!/.3
42    (3!)!! - 3·3 + 3 = 3!·3! + 3 + 3 = 3!·(3! + 3/3) = 33 + 3·3 = (3!)3/3 + 3! = 33/.3 - (3!)!!
45    (3!)!! + 3 - 3 + 3 = 3·(3! + 3!/3)!!
46    (3!)!! + 3 + 3/3 = (3 + 3)!! - 3!/3 = (3!)!! - Ö(3 + 3/3) = (3!)!! - Ö(3! - 3!/3)
48    (3!)!! + 3! - 3 - 3 = ((3!)!! + (3!)!! + (3!)!!)/3 = 3·Ö(3·(3!)!!) = 3·3·3! - 3!
66    33·3!/3 = 33 + 33 = (3!)!! + 3·3! - 3 = Ö(3·(3!)!!)·3! - 3! = 3·3!/.3 + 3!
69    (3!)!! + 3! + 3! + 3! = Ö(3·(3!)!!)·3! - 3 = (3!)!! + 33 - 3! = 33 + 3!·3!
72    3·3·(3!)!!/3! = (33 - 3)·3 = (3!)!! + 33 - 3 = 3!·3! + 3!·3! = (3!)3 - 3·(3!)!! = (3!)! - 3·(3!)3 = 3!·3!/.3 - (3!)!! = (3 + 3/3)!·3

Corrected expressions are in blue. One correct expression has been added for number 30. The incorrect expression for number 48 has been corrected and shifted to number 72:

28    33+3/3 = {3·3/.3-Ö3} = 33 + 3/3 = (Ö((3!)!!) + 3!·Ö((3!)!!)/Ö3 - 3
30    3·3·3+3 = 3!·3! - 3 - 3 = 33 + 3! - 3 = 3·3·3 + 3 = ((3!)!! + (3!)!! - 3!)/3 = (3!)!! - 3!·Ö(3·3)  = (3!)3/3! - 3!
33    33-3+3 = 33/3·3 = 33 + 3 + 3 = 3!·3! - 3! + 3 = (3!)3!/3 - 3 = 3·Ö(3·(3!)!!) - 3 = ((3!)!! + (3!)!! + 3)/3 = (3!)3/3! - 3
34    33+3/3 = 3!·3! - 3!/3 = ((3!)!! + (3!)!! + 3!)/3
39    33 + 3 + 3 = 3!·3! + 3! - 3 = (3!)!! - 33!/3 = (3!)3!/3 + 3 = 3·Ö(3·(3!)!!) + 3 = (3! + 3!)·3 + 3 = (3!)3/3! + 3
40    (3 + 3!/3)!/3 = (3!)!! - 3! - 3!/3 = (3!)!! - (3!/3)3 = 3!/3·3!/.3
42    (3!)!! - 3·3 + 3 = 3!·3! + 3 + 3 = 3!·(3! + 3/3) = 33 + 3·3 = (3!)3/3! + 3! = 33/.3 - (3!)!!
45    (3!)!! + 3 - 3 - 3 = 3·(3 + 3!/3)!!
46    (3!)!! - 3 + 3/3 = (3 + 3)!! - 3!/3 = (3!)!! - Ö(3 + 3/3) = (3!)!! - Ö(3! - 3!/3)
48    (3!)!! + 3! - 3 - 3 = ((3!)!! + (3!)!! + (3!)!!)/3 = 3·3·3! - 3!
66    33·3!/3 = 33 + 33 = (3!)!! + 3! + 3! + 3! = Ö(3·(3!)!!)·3! - 3! = 3·3!/.3 + 3!
69    (3!)!! + 3·3! + 3 = Ö(3·(3!)!!)·3! - 3 = (3!)!! + 33 - 3! = 33 + 3!·3!
72    3·3·(3!)!!/3! = (33 - 3)·3 = (3!)!! + 33 - 3 = 3!·3! + 3!·3! = (3!)3 - 3·(3!)!! = (3!)! - 3·(3!)3 = (3 + 3)·Ö(3·(3!)!!) = 3!·3!/.3 - (3!)!! = (3 + 3/3)!·3

As for the four 5's post, that's about 300 expressions. I already checked them twice, but I still found some minor errors. I have to do it until I find none. Once more, I am sorry for causing you this trouble.

Vladimir

Current research also covers classroom communication, social, cultural, and linguistic influences on the teaching and learning of mathematics, and of course its assessment. According to Ness,

'Ness' should be 'Niss'
Thankyou

sfwc
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