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Daily Maths Challenges
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Share your cool maths problems.
Complete a challenge:
- Post your solution in comments, if it is exactly the same as OP's solution, let us know.
- Have fun.
Post a challenge:
- Doesn't have to be original, as long as it is not a duplicate.
- Challenges not riddles, if the post is longer than 3 paragraphs, reconsider yourself.
- Optionally include solution in comments, let it be clear this is not a homework help forums.
- Tag [unsolved] if you don't have a solution yet.
- Please include images, if your question includes complex symbols, attach a render of the maths.
Feel free to contribute to a series by DMing the OP, or start your own challenge series.
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An 8x5 rectangle. If the bottom left corner is considered (0, 0), then two lines are drawn within the rectangle, from (0, 4) to (8, 1) and from (1, 5) to (7, 0). The smaller two regions of the four these lines cut the rectangle into are shaded. What is their combined area?
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- Evaluate
SUM(1/(n + n^2))from n = 1 to infty
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- Show that
arcsin y = arccos xis the equation of a circle. - Note that the equation of a circle is
x^2+y^2=1.
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The image is of a large unit square with five smaller disjoint shaded squares contained entirely within it. The five smaller squares are congruent. Four of them are at each corner of the large square. The fifth is in the center, rotated diagonally, so the center of each of its sides is touched by the vertex from one of the other four squares. You are given that the common length for the five smaller congruent squares is (a-sqrt(2)) / b, where a and b are positive integers. What is the value of a + b?
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Prove that the sum of the reciprocals of the Fibonacci numbers up to infinity converges to a finite value.
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- Estimate 10000!
- Give our answer in form exp{a ln(a) - b ln(b) + c}
- Hint: e
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- Proof that the infinite sum 1+2+3+4+... = -1/12
- You may assume that 1-1+1-1+... = 0.5
