Math Is Fun Forum

See post #9 for why (via Pythagoras) BF ≈ 1.414cm long instead of the 2cm that it should be.

Looks to me like it's a perspective conundrum, as with some optical illusions.

In the image below (which I drew in Geogebra), the left-hand image looks like a cube (but the measurements tell me it's not), and the right-hand image is a cube according to the measurements (but it certainly doesn't look like one)!

I even printed the image to check the measurements, got my ruler out, and..........they're all correct!

There are other illusions, too: eg,
   1. The green and red squares are congruent, but the green square seems to be larger than the red square.
   2. Lines AF & BG are parallel, but don't seem to be.
   Similarly with the right-hand image...

Re the congruent-squares illusion: I guess that my brain's probably thinking perspectively, and 'knows' that in these 3d images the rear square should appear smaller than the front square. With that not being the case (the squares being congruent), my brain then 'sees' the rear square as larger than the front square. Similarly with the 'non-parallel' lines...
 

I followed your instructions from post #6 and changed https://i.imgur.io/7uB3NEI_d.webp? to https://i.imgur.io/7uB3NEI.jpeg, but that didn't work. Neither did other changes I tried.

Btw, webp, which appears in your url, is a valid image extension recognised as such by Imgur. And so https://i.imgur.com/t5wC8Hg.webp works fine, just like the other 4 image files that I listed in my post #10.

Which image does https://i.imgur.io/7uB3NEI_d.webp? refer to?

Also, what did you change the url to that worked, and did you test it in img tags?

Does the info in this link help any? Direct link to image on mobile

I'm rather hamstrung trying to help resolve this issue, not having a smartphone!

Two things:

1. Image tags and the url within the image tags can't contain spaces, but yours do, and must be removed. I've marked the offending spaces with a red x:
    (a) before and after the url: xhttps://imgur.com/gallery/4Gh1VYyx
    (b) in the opening tag: [ximgx]
    (c) in the closing tag: [x/ximgx]
    Note: Image tags are a BBCode formatting option that must obey a specific syntax for them to work.  See example here: BBCode (near the bottom of the 'Links and images' box).

2. The url is to a webpage, and although that page contains the image (+ other stuff), the url must be to the image itself.

See the following...

And from the image in my post #14:
     "Tip: The URL starts with https://i.imgur.com, and ends with an ‘image extension’ (eg, ‘gif’, ‘jpeg’, ‘jpg’ or ‘png’)."

Your https://imgur.com/gallery/4Gh1VYy doesn't start with https://i.imgur.com, and doesn't end with an image extension...

I read into your post that you've worked out how to obtain an image link, and to paste it, with your Android! Correct?

If so, all that's left now is for you to enclose the url in img tags to display the image...like so:

[img]image url[/img]

Sorry, I can't give any practical help because I only have a PC and laptop, not a smartphone.

Try this search on YouTube: "How to copy image url on android". That brings up many tutorials, and hopefully you'll find one that suits.

However, that will take some doing! Some have presenters with very strong accents, some in non-English, some with awful music and no vocals, some with irrelevant introductory content to ignore...etc, etc.

I couldn't find a really good video tutorial, but here are two of the better ones (though not all that easy to follow!):

how to copy Google images into url in android (many positive comments from posters)
How To Copy Image Link From Google In Mobile (positive poster comments, but one said this: "Well but you don't need to open image in new tab you can simply press on preview image and copy the link")

I found the first one easier to understand, but for your purposes, it really starts at the 1:00 minute mark. You'll probably need to watch it several times. Also, you may need to pause & replay some sections where the presenter's too quick, so that you can see the particular action she's performed on her phone.

I had thought that amnkb's tutorial would've got you over the line...

Hi amnkb,

For an image to display on this forum, the link must be to the actual image file: ie, it has to contain an 'image extension' at the end of the filename (such as '.jpg' or '.png')...as per the BBCode example below.

The OP's link is an Imgur webpage url, and hence no image will display here.

The webpage link from Post #3 (https://imgur.com/a/hQDSFH4) gives me a '404' error. Maybe the link worked for Bob initially, but if it did, I wonder if it still does. I only tried it today...

The following instruction and example are from the BBCode instruction page that you can access by clicking on the 'BBCode' button under the Message box into which you type a post (or by clicking here: BBCode), and then scrolling to the bottom of the 'Links and Images' box:

If you want to display an image you can use the img tag. The text appearing after the "=" sign in the opening tag is used for the alt attribute and should be included whenever possible.
[img=FluxBB bbcode test]http://www.mathisfunforum.com/img/test.png[/img]

That code produces

Hi Checker 555!

I went to the Checkers game, and also got a pop-up that prevented play.

However, my pop-up has a 'New Game' button at the bottom, and clicking that makes the pop-up disappear and starts a new game.

The pop-up also has a 'Close' button next to the 'New Game' button, but clicking that only closes the pop-up. To start a game you'd then have to click the 'New Game' button above the playing board.

I hope your pop-up's the same as mine!

Hi Bob...the guitarist is Gerhard Gschossmann.

And here's the link to the recording I used: Gerhard Gschossmann - 'Summertime' (George Gershwin) guitar solo fingerstyle

That version is played at the song's correct tempo, with good feeling and expression...which makes my Geogebra soundtrack sound rather chipmunkeyish.

Here's a vocal clip of the song: GEORGE & IRA GERSHWIN 'Summertime' HAROLYN BLACKWELL ('Porgy & Bess'). Very moving!!

Hi Bob,

Here's a little video of an animation of the range of non-symmetrical scenarios obtained by running Point B along line AP:
Non-symmetrical range (video)

Edit: Sorry, I lied.   The range includes the symmetrical scenario I mentioned in my previous post. The symmetry appears 3 times: at the start of the video, at the 14-second mark, and at the end of the video. Each time, N is smack in the middle of the square and the 4 vertices are 67.5°.

Hi Bob,

I suspect that making a square with those extensions will help!

I've redrawn the diagram:

It also 'happens' that PO runs through N...and, of course, PO divides right angles APD and DOA into 45s.

...and there are umpteen similar triangles (but I haven't seen anything yet).

Hi tony123;

Too tough for me, so I tried trial and error in Excel and got this:

Hi jiaoqian, and welcome to the Forum!

I did this puzzle many years ago, and, like you, could not resolve the French/Brazilian cocoa/tea issue.

That means there are two solutions, which, for me, is disappointing.

I've done many of these types of logic puzzles, and the Ships Puzzle is one of the very few I've come across that has multiple solutions...