a rope around the earth

Have a guess! (brain teaser)
Imagine pulling a rope around the globe (which is a perfect sphere) and tensing the rope tight. Now you add 10 meters to the rope and distribute the rope around the globe so that it is equidistant from the globe (see sketch above).
➽ What is the distance x between the globe and the rope?
➽ Do you think it is enough height for a fly to crawl down through?

Answer:
In the calculation above you can see that the distance is 1,59 m!!

And the astonishing point is: You can do the same with an orange (fruit) and it will give the same result!!
Well, mathematically not really remarkable, but imaginatively it's astonishing! :-)

~~... and there is an additional point that you may have noticed: on the globe above GB is missing. So the Brexit also is solved!~~ ;-))
Due to several complaints I have reinserted the British Isles. ;-))

By the way:, have you also noticed that longer texts are no longer completely translated by the translator?

According to ➽ Sami Serola's riddle. ...

, Ruebenkraut, Diane Putnam, Ruesterstaude and 6 other people have particularly liked this photo

40 comments - The latest ones

polytropos ^club

I replaced the sketch and added GB and Ireland! ;-)

5 years ago. Edited 5 years ago.

Gudrun ^club has replied to polytropos ^club

Irland hätte auf jeden Fall drauf sein müssen, auch wenn der Brexit schon eingetreten wäre;-)

5 years ago.

polytropos ^club has replied to Gudrun ^club

Gudrun, habe ich dank einem lupenreinen Ersetzen noch hingekriegt! ;-)
Aber "Ersetzen" kann man glaubs nur einmal machen, oder? Falls der Brexit dereinst Wirklichkeit wird, kann ich das hier nicht mehr korrigieren. ;-)

5 years ago.

Gudrun ^club has replied to polytropos ^club

Ich glaube, du kannst so oft Ersetzen, wie du willst;-)

5 years ago.

polytropos ^club has replied to Gudrun ^club

Gudrun, muss ich mal versuchen :)

5 years ago.

Sami Serola (inactiv… ^club

1,57 m! That is astonishing! =O

5 years ago.

polytropos ^club has replied to Sami Serola (inactiv… ^club

Yes, it is!
And the most astonishing fact is, that it is the same result with an orange! :-)

5 years ago.

Sami Serola (inactiv… ^club has added

You could have created A and B options to similarly give answers to wrong and right choices ;-)

And then the first question page should of course be public.

Anyway, here's an fiction story, which you may find interesting. Follow the signs! ;-)

www.ipernity.com/doc/serola/46626226

5 years ago.

Sami Serola (inactiv… ^club has replied to polytropos ^club

So, if I add 10 meters on the rope tightened around an orange, it then after the addition is 1,57m away from the orange surface?! Astonishing indeed! =O

5 years ago. Edited 5 years ago.

polytropos ^club has replied to Sami Serola (inactiv… ^club

Exactly!! :-)

5 years ago.

polytropos ^club has replied to Sami Serola (inactiv… ^club

Yes, good idea! I'll think about, when I'll have a little more time. :)

Yes, interesting link! I'll have a look later on :)

5 years ago.

Daniela Brocca ^club

Warum sollte man so was tun, frage ich mich? :-))

5 years ago.

polytropos ^club has replied to Daniela Brocca ^club

Daniela, aus Freude an Gedankenexperimenten :-))

5 years ago.

Eva Lewitus ^club

Nobody mentions the poor fly!
Why should it want to crawl down, or through?

5 years ago.

polytropos ^club has replied to Eva Lewitus ^club

Eva, this is only a distraction to mislead the reader concerning the dimensions :-)
No animal were harmed during the thought experiment. :)

5 years ago. Edited 5 years ago.

Eva Lewitus ^club has replied to polytropos ^club

:-)

5 years ago.

Herb Riddle ^club

Oh dear, my head hurts a little -maybe because of the maths or perhaps it is the disappearance of the country that I thought I was residing in :)

5 years ago.

polytropos ^club has replied to Herb Riddle ^club

Herb, I'm terribly sorry about the unlucky disappearance of your homeland, but it was a quick hand sketch I had to draw from memory! But as you can see I replaced the sketch with a completed version :-)
Concerning the math: it may looks a bit complicated, but it's only a simple circle calculation. :)

5 years ago. Edited 5 years ago.

Boarischa Krautmo ^club

super Zeichnung, dafür einen Stern.
das Problem habe ich mir erlaubt symbolisch zu lösen ;-)

5 years ago.

polytropos ^club has replied to Boarischa Krautmo ^club

B.K., du schreibst ja wie ein Arzt! ;-))
Aber danke für den rein mathematischen Lösungsansatz. Ich versuchte es auf dem "volkstümlichen" Weg ;-))

5 years ago.

Boarischa Krautmo ^club has replied to polytropos ^club

ja, deine Skizze ist viel ordentlicher ;-)
der volkstümliche Weg hat halt bei der Orange das Problem, wieder von vorne anfangen zu müssen.....

5 years ago.

polytropos ^club has replied to Boarischa Krautmo ^club

B.K., naja, ganz von vorne nicht. Man muss nur eine neue Zahl ( z.B. 0,10, für d = Orange) in einen etwas gedächtnisfähigen Taschenrechner eintippen und fertig ist! ;-)

5 years ago.

Berny ^club

Wirklich sehr erstaunlich....und originell. So lustig kann Mathe sein ;-)

5 years ago.

polytropos ^club has replied to Berny ^club

Berny, genau! Und man kriegt auch noch Geografieunterricht ;-)

5 years ago.

Ruesterstaude ^club

Die Rechnung stimmt! Man braucht nur 10 durch pi zu dividieren!

5 years ago.

polytropos ^club has replied to Ruesterstaude ^club

Ruesterstaude, ja, Mathe kann so simpel sein! :-)

5 years ago.

Diane Putnam ^club

Oh yes, poor little Ireland! Well, I have no idea what this is all about, but I like the elegance of it. I also love the rough sketch of the continents, especially Italy's crazy boot! ;-)

5 years ago.

polytropos ^club has replied to Diane Putnam ^club

Diane, it is only a matter of explaining the human inadequacy of estimating certain circumstances. Or could you have imagined that only 10 meters (11 yards) more rope around the earth make so much (1,74 yard)?
I have recognized for instance that hatter must be a very exact profession! Only a few millimeters more of circumference and the hat does not fit on the head anymore. :)

5 years ago.

Ruebenkraut ^club

Tolle Idee und Umsetzung! Ein Glück, dass unser Kopf keine exakte Kugel ist, sonst würden nur maßgefertigte Hüte passen. So wie es ist, bleibt der einigermaßen passende Hut dann meist doch irgendwo hängen, z.B. auf den Ohren ;-)

5 years ago.

polytropos ^club has replied to Ruebenkraut ^club

Ruebenkraut, genau, darum trägt Nicki Lauda ein Baseball Cap ;-))
Danke für deine tiefschürfenden Betrachtungen zu diesem Thema! :-)

5 years ago.

David G Johnson ^club

Polytropos'..... I enjoy these facts and physics... thanks for posting... Here's another >
........and I find it difficult to convince other people of this fact.......

''That a bullet fired from a ..level.. gun..'' ''will fall to the ground at exactly the same time
as a bullet dropped vertically - (at the same time of firing - and the same height) of the gun muzzle'' // Meaning..despite the velocity of the fired bullet...gravity still rules.
Cheers from David J'

5 years ago.

polytropos ^club

David, I hope I understood it correctly. One bullet is fired vertically and the other horizontally, and both bullets will fall at the same time to the ground?

5 years ago.

David G Johnson ^club

Thanks for your interest...All credit to a pal of mine - who told me this fact many years ago.

It doesn't matter how high the 'level gun' is off the ground. 1m. 2m. 3m. 4m. etc.
The bullet is fired level and will travel some distance and fall to ground.
The second bullet is '..dropped vertically by hand..' at the gun muzzle at the
same moment of firing..
astonishingly gravity pulls both bullets to earth at the same rate.
I found a decent video'.. on Youtube'... the mathematical formula's aren't essential to follow
unless you enjoy that kind of thing :-)
Cheers - and best wishes... from David J'..

www.youtube.com/watch?v=_-soNrVIb8U

5 years ago.

polytropos ^club has replied to David G Johnson ^club

Hey, David, thanks a lot for the explanations! The video is very descriptive! The formulas aren't so difficult, but I admire how professor Anderson is able to write so fast and clean in mirror image handwriting on that glass pane! :-))

5 years ago.

David G Johnson ^club has replied to polytropos ^club

Howdy.... 'polytropos'.... further to our technical chats.. I took another look at ..Prof' Anderson'.. and saw that he appeared to be writing left handed.. So I wondered if what was being seen was all recorded through some sort of mirror system.. and he was actually writing normally.. not mirror image. I searched further video's of his.. and came across the answer... Cheers from David J'.. UK
www.youtube.com/watch?v=CWHMtSNKxYA&t=25s

5 years ago. Edited 5 years ago.

polytropos ^club has replied to David G Johnson ^club

David, oh, thanks a lot for that link! Now I see it! What a clever invention!

5 years ago.

Guido Werner ^club

Wow, jetzt wird sogar auf ipernity über Kugeloberflächen diskutiert. Dabei dachte ich, dass ich das hinter mir gelassen habe:

kups.ub.uni-koeln.de/841/1/wernerguido.pdf

Viel Spaß beim Lesen. :-))

5 years ago.

polytropos ^club has replied to Guido Werner ^club

Guido, hm, ich musste schon bei Immersion googlen und nachdem ich erfahren hatte, dass es sich dabei um eine Funktion mit injektivem Integral handelt, musste ich das Blatt kurz beiseite legen. Als ich danach weiterlas, frug ich mich, ob es sich dabei nicht um arbiträr digital evozierten Zufallstext handelt! ;-))
Interessant ist auch, dass bei meinem letzten Bild auch ein geosphärisches Problem angesprochen wird; nämlich die Bestimmung des Winkels (qibla) nach Mekka von einem beliebigen Punkt der Erde aus. :-)

5 years ago.

Guido Werner ^club

Ich verstehe ja selbst nicht mehr, was ich damals geschrieben habe. :-)) Aber Eines weiß ich dann doch noch: Eine Immersion hat ein injektives Differential, nicht Integral. :-)

Zu dem Problem des Architekten mit der Ausrichtung nach Mekka: Er hätte die Moschee einfach am antipodischen Punkt von Mekka bauen sollen, also an der exakt gegenüberliegenden Stelle auf der Erdkugel. Von dort weist nämlich jede Richtung nach Mekka (so wie am Nordpol jede Richtung zum Südpol weist). Beim Bau einer Moschee kann man dort also nichts falsch machen. Einziges Problem: Das ist mitten im Südpazifik und es gibt dort nur Wasser.

5 years ago.

polytropos ^club has replied to Guido Werner ^club

Oups, ja, Differential, nicht Integral. Da hat wohl irgend eine mentale Injektion mein differenziertes Denken disturbiert. ;-))

Mit (nur) diesem einen Standort wären die Muslime wohl nicht ganz einverstanden. Sie pflegen ja ein eher recht expansives "Geschäftsmodell". ;-)

5 years ago.

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