# [EN] # Welcome to the new challenge series for your brain! Sometimes I have to doubt my own brain. I was sitting here thinking long and hard what content could be actually good for the proof of brain tag. Maybe some sort of riddle? But looking at how sophisticated riddles people like @one.alfa or @friendlymoose make, there was already good content on hive that I would have to compete with. Just now I had the enlightenment: Mathematical Proofs. I studied math for a few semesters and I was actually quite good at doing Proofs which is all you do as a mathematician. I have posted Proofs on hive in the past and while they only garnered medium attention, I think setting up a challenge with prizes will lead to a lot more normal people engaging, who haven't already studied math, physics or IT . I will make a separate post about the Beauty of Proofs and how to do them. But for those who already know what I am talking about: correctness is of course the condition to qualify but what counts is the beauty of the Proof. And more importantly how I evaluate the beauty. I prefer number-based Proofs over graphical Proofs and text-based Proofs over number-based Proofs. At least in general.  *proofofbrainio allowed me to use this lovechild of our avatars* ------------ # This weeks Challenge ---------- Proof the sentence of Pythagoras: a²+b²=c² ---------- # Prize Money ----------- First place: 10 POB Second place: 5 POB Entries are accepted until 6 days after this post has been punlished. You can comment your Proof or make a separate Post that you link in the comments. # [DE] # Willkommen zum neuen Gewinnspiel mit Grips! Manchmal zweifel ich auch an meinem Grips, wenn ich daran denke wie lange ich mir den Kopf darüber zerbrochen habe, was ich für Proof of Brain für Content machen. War auch die ganze Zeit in die Richtung Gewinnspiel am Denken, aber da gibts ja schon viel Zeug auf der Kette. Dann hats mich getroffen: Mathematische Beweise. Ich hab mal ein bisschen Mathe studiert und war mal echt gut in Beweisführung. Ich bin davon überzeugt, dass die Fähigkeit mathematisch zu beweisen, einen eine ganz andere Sichtweise auf die Mathematik gibt und das logische Denken schärft. Mit einem Gewinnspiel kann ich jetzt auch hoffentlich endlich die motivieren sich mit dem Thema zu befassen, die den ganzen Schmarn nicht schon aus dem IT Studium kennen. Ich werde einen separaten Post darüber schreiben, wie man einen Beweis führt und warum es sowas wie Schönheit in kalten mathematischen Beweisen geben kann. In meiner Challenge wird auch nach Schönheit beurteilt, Korrektheit ist lediglich eine Grundvoraussetzung. Für die, die wissen wovon ich rede: ich finde formelle Beweise besser als Grafische und Informelle besser als Formelle. Jedenfalls als Faustregel. ------------------- # Die Challenge der Woche --------------- Beweise den Satz des Pythagoras: a²+b²=c² ------------ # Preisgeld Erster Platz: 10 POB Zweiter Platz: 5 POB Einsendeschluss ist 6 Tage nach Veröffentlichung dieses Posts. Ihr könnt euren Beweis in die Kommentare schreiben oder einen eigenen Post machen, den ihr in den Kommentaren verlinkt. --- <center><sub>Posted via [proofofbrain.io](https://www.proofofbrain.io/@thatgermandude/proof-in-math-proof-of-brain-challenge-1-de-en)</sub></center>
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Haha. Coole Idee. Aber wir sind hier alle nur um uns gegenseitig einzureden, dass wir ein Gehirn haben. Nicht um es wirklich zu beweisen. :D Ich hab Mathe für Wirtschaftswissenschaftler 1 und 2 gemacht. Aber so sehr vermisse ich es nicht. Ein paar Schach-Puzzle oder Rätsel wären auch eine gute Idee, für die Nichtmathematiker. --- <center><sub>Posted via [proofofbrain.io](https://www.proofofbrain.io/@antonym/qrvnlk)</sub></center>
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> Aber wir sind hier alle nur um uns gegenseitig einzureden, dass wir ein Gehirn haben. Jaja, das gute alte Echo Chamber hive. Wie sie alle den POB Markt stürmen um endlich ein Beweis für ihr Hirn zu haben :D. Mathe für Wirtschaftler ist keine Universitätsmathematik. Ist jetzt kein böses Vorurteil oder so, aber ihr macht einfach was ganz anderes. Glaub mal selbst Informatiker die an der Schule mal Mathe-Asse waren stönen bei uns wofür se denn den Schwachsinn alles brauchen. Ich werde die Tage mal einen Artikel zur Schönheit der Mathematik machen. Es hat auch was mit Logik und Weltverständnis zu tun. Vielleicht holts dich ja ab. Anders als das 1x1 in der Schule lernen kann das hier echt Spaß machen. Außerdem können die arroganten STEMler nicht mehr auf dir rumhacken, wenn du Uni-Mathe verstehst. Ist immerhin das schwerste Fach.
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Working on a proof by exhaustive search, but this challenge might end before my proof is complete 😂 --- <center><sub>Posted via [proofofbrain.io](https://www.proofofbrain.io/@chasmic-cosm/qrvcdi)</sub></center>
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You have almost a whole week, so take your time. Looking forward to your proof!
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It was just a joke... exhaustive search would mean checking that the statement holds true for every possible right angled triangle. I rather quite like Euclid's construction of this proof, but don't just want to copy. Might think about it a while and try put together a real proof that doesn't involve checking an infinite number of triangles... --- <center><sub>Posted via [proofofbrain.io](https://www.proofofbrain.io/@chasmic-cosm/qrvdez)</sub></center>
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I would like to exclude myself from the prize but have a go for fun if that's ok ;) lets take a diffrent approach, how do define distance between any two points (x1,y1) and (x2,y2) ? ((X2-x1)^2 + (y2-y1)^2))^0.5 = distance Or distance ^2 = (X2-x1)^2 + (y2-y1)^2) In a right angle triangle , distance is C, the difference between x points is length a and y points is length b
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Once you enter a comment you have entered the Challenge! Muahahhahahahah! You are doing the classic beginner mistake of using Pythagoras to prove itself. You can calculate the distance on a coordination field this way because you know Pythagoras is true not the other way around. Do you understand what I am saying? It is a rough hurdle to take, dw.
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Ok fine then, I'll use relatively next time ;p no I get what your saying just never relasied pythagoras lead to this !
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Ok new idea assuming area all ready given for a square and triangle. Ok imagine 4 identical triangles, each with an area of ab/2 because they are right angles(×we will use this layer). We arrange the triangles into a square shape so c faces outwards on all sides. We now have a square with a second smaller sqaure cut out inside it. We know one thing already, the area of this shape is 4 triangles worth , 4 x ab/2 to be exact or 2ab We also know the area of this shape is the outer square is c x c or c^2 minus the inner square undefined C^2 minus inner square = 2ab The inner square is made up of the length A less length b which buts against it. So it is (a-b)^2 Plugging it back in you get C^2 -(a-b)^2 = 2ab Which unfolds into c^2 = a^2 + b^2
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Correct! I had to put the graphics on a side tab to get it... :D .But yes this one of the more popular Proofs for Pythagoras and you explained it really well, to a degree where I understood and even if you googled it, you made sure you understood it as well. Thank you for participating!
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Thanks didn't google but I did have an advantage... I did a physics degree:p so just had to sit down and push triangles around for awhile until I found a different formula (area) that I could build on
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Congrats you won 10 POB
author | thatgermandude |
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Thank you! Great comp :)
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Ich bin raus, vor 10 Jahren hätte ichs glaube noch gekonnt.
author | mein-senf-dazu |
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Ach komm schon... die guten alten grauen Zellen wieder etwas in Schwung bringen :)
author | thatgermandude |
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Ich werde mal überlegen, aber ich glaube das wird nichts. Langt dir 3²+4²=5² 😁😁😁
author | mein-senf-dazu |
---|---|
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I don't really understand what the challenge is? It is the Pythagorean theorem where a and b are the legs. c would be the hypotenuse. --- <center><sub>Posted via [proofofbrain.io](https://www.proofofbrain.io/@yeckingo1/qrv5wc)</sub></center>
author | yeckingo1 |
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deeclown | 0 | 3,724,612,858 | 100% | ||
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yes. I didn't want to tackle the whole 'what is a proof'-topic in this post because it is a tough nut to crack. I will do a follow up post where I explain the concept in detail, but for now feel free to ask anything.
author | thatgermandude |
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steinhammer | 0 | 919,958,754 | 100% |
author | lucylin |
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