This week's maths problem

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Problem of the week

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On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 11th. July 2024.

German version - Italian version - French version - Spanish version  Hungarian Version Russian version  --> 中文/Chinese <-- --> Ελληνικά   <--

Series 66

problem 792


Dürer letter:

792 792 rot

‘Hello Grandad, you've brought us another beautiful letter,’ said Maria and Bernd. ‘But the construction doesn't exactly look easy,’ said Mike. ‘That's right!’
Start with a square ABCD with side length a (here a = 10 cm). The points E, F, G and H are the centres of the sides of the square. The centre points are joined together and lead to point I. Points S and N are at a distance of a/30 from the sides. Point J is at a/30 distance from I. Point M is at a/10 distance from I. To draw the blue and green circles, you have to construct their centres P, Q, U and T respectively. The circles with the centres V and E_1 each have a radius of a/10. The drawing clearly shows how to construct the points of the right-angled triangles that form the vertices of the letter.
What is the area and circumference of the blue and green circles? Complete arithmetic path - 8 blue points
What are the perimeter and area of the triangle A_1 F_1 D_1? Solution by calculation 8 red points (Alternatively, a constructive solution would be awarded 4 red points).

Deadline for solution is the 11th. July 2024.




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Thomas Jahre
Paul-Jäkel-Straße 60
09113 Chemnitz


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Thomas Jahre
Chemnitzer Schulmodell
Stollberger Straße 25
09119 Chemnitz
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