User Franklin Pezzuti Dyer

168

230

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11

answers

18k

views

“Integral Milking”

Dec 11 at 20:48 clathratus 13.7k

37

86

votes

4

answers

9k

views

Do numbers get worse than transcendental?

definite-integrals soft-question irrational-numbers transcendental-numbers

Dec 27 '17 at 2:58 richard1941 727

36

61

votes

6

answers

6k

views

Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$…

functions function-and-relation-composition

Jul 15 '17 at 23:32 amWhy 200k

19

51

votes

3

answers

1k

views

What numbers can be created by $1-x^2$ and $x/2$?

functions dynamical-systems recreational-mathematics function-and-relation-composition

Oct 17 '18 at 14:42 Franklin Pezzuti Dyer 34.7k

7

36

votes

3

answers

3k

views

Painting the plane, and finding points one unit apart

geometry graph-theory contest-math coordinate-systems

Oct 7 '18 at 23:04 hmakholm left over Monica 268k

22

32

votes

3

answers

667

views

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

integration definite-integrals recreational-mathematics functional-equations upper-lower-bounds

May 18 '18 at 14:00 Julian Rosen 14.8k

5

29

votes

2

answers

2k

views

Functional equation: what function is its inverse's reciprocal? [duplicate]

inverse functional-equations inverse-function

Jan 6 '18 at 1:00 Gottfried Helms 31.1k

9

25

votes

7

answers

642

views

When does $\sqrt{x+\sqrt{x+1+\sqrt{x+2+…}}}=0$?

roots radicals nested-radicals

Aug 27 at 16:37 Dark Malthorp 3,799

13

25

votes

7

answers

1k

views

Examples of simple but highly unintuitive results? [closed]

soft-question recreational-mathematics intuition big-list

Jul 1 at 16:59 Zhuli 2,319

6

25

votes

1

answer

534

views

Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$?

integration definite-integrals logarithms symmetry

Jun 5 '19 at 14:49 Zacky 21.8k

9

25

votes

1

answer

950

views

Strange functional equation: $f(x)+f(\cos(x))=x$

real-analysis functional-equations

Sep 5 '18 at 14:39 Community♦ 1

3

22

votes

1

answer

629

views

Series involving Fibonacci Numbers: $\sum_{k=1}^\infty \frac{1}{F_kF_{k+1}}$

sequences-and-series fibonacci-numbers telescopic-series

Dec 28 '17 at 11:07 user90369 11k

12

21

votes

5

answers

545

views

Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

integration definite-integrals improper-integrals recreational-mathematics functional-equations

Jun 20 '18 at 23:18 G Cab 30.3k

8

21

votes

3

answers

387

views

Minimum values of the sequence $\{n\sqrt{2}\}$

recurrence-relations irrational-numbers fractional-part almost-periodic-functions

Dec 26 '17 at 10:10 Ewan Delanoy 55.6k

11

20

votes

2

answers

922

views

Peculiar Sum regarding the Reciprocal Binomial Coefficients

sequences-and-series definite-integrals summation binomial-coefficients closed-form

Jul 25 '17 at 21:56 Olivier Oloa 117k

2

18

votes

2

answers

812

views

Crazy Iterated Square Roots

sequences-and-series radicals function-and-relation-composition nested-radicals geometric-series

Jul 12 at 20:05 Anonymous 303

4

18

votes

1

answer

408

views

Average Distance Between Zeroes of $\sin(x)+\sin(x\sqrt{2})+\sin(x\sqrt{3})$

real-analysis periodic-functions almost-periodic-functions

Sep 26 '19 at 10:32 Paul 2,507

5

18

votes

1

answer

376

views

Number of real zeroes of iterated polynomial: $x^3-2x+1$

combinatorics polynomials roots function-and-relation-composition

Oct 23 '18 at 14:55 G Cab 30.3k

7

17

votes

3

answers

5k

views

Rationalizing the denominator having square roots and cube roots

rationalising-denominator

Apr 28 '19 at 5:45 Teresa Lisbon 59.4k

6

15

votes

2

answers

348

views

Recurrence $a_{n}=a_{\lfloor 2n/3\rfloor}+a_{\lfloor n/3\rfloor}$

sequences-and-series limits recurrence-relations asymptotics

Dec 19 at 17:39 Sungjin Kim 16.1k

8

14

votes

3

answers

552

views

Sum of $\{n\sqrt{2}\}$

summation random-variables asymptotics irrational-numbers fractional-part

Apr 19 '19 at 21:52 Community♦ 1

7

14

votes

1

answer

181

views

Number of real roots of an iterated quadratic: $x^2-3/2$

combinatorics polynomials roots function-and-relation-composition

Sep 29 '18 at 21:08 Peter Taylor 12.7k

9

14

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2

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740

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Integral Representation of the Dottie Number

trigonometry definite-integrals constants fixed-points

Jan 22 '18 at 19:51 Hans 7,658

6

13

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3

answers

241

views

How many closed paths with the operations $+1$, $-1$, and $\times 2$?

sequences-and-series combinatorics asymptotics markov-chains

Sep 4 '19 at 14:59 David E Speyer 53.3k

1

13

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5

answers

2k

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Does continuity depend on the distance function?

general-topology elementary-set-theory continuity

Jul 12 '17 at 18:46 Andrew 262

8

13

votes

0

answers

733

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Omega Constant Integral

integration definite-integrals closed-form lambert-w

Jun 22 '17 at 7:25 tired 11.7k

4

13

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6

answers

3k

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Geometry Construction Problems

geometry euclidean-geometry geometric-construction

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12

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5

answers

555

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Trig identities analogous to $\tan(\pi/5)+4\sin(\pi/5)=\sqrt{5+2\sqrt{5}}$

trigonometry prime-numbers modular-arithmetic gauss-sums algebraic-numbers

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10

12

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6

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Interesting Proofs about Metric Spaces?

real-analysis general-topology metric-spaces soft-question

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6

12

votes

3

answers

601

views

Extinction probability in a population with competition

probability limits stochastic-processes asymptotics

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226 Questions

“Integral Milking”

Do numbers get worse than transcendental?

Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$…

What numbers can be created by $1-x^2$ and $x/2$?

Painting the plane, and finding points one unit apart

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

Functional equation: what function is its inverse's reciprocal? [duplicate]

When does $\sqrt{x+\sqrt{x+1+\sqrt{x+2+…}}}=0$?

Examples of simple but highly unintuitive results? [closed]

Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$?

Strange functional equation: $f(x)+f(\cos(x))=x$

Series involving Fibonacci Numbers: $\sum_{k=1}^\infty \frac{1}{F_kF_{k+1}}$

Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

Minimum values of the sequence $\{n\sqrt{2}\}$

Peculiar Sum regarding the Reciprocal Binomial Coefficients

Crazy Iterated Square Roots

Average Distance Between Zeroes of $\sin(x)+\sin(x\sqrt{2})+\sin(x\sqrt{3})$

Number of real zeroes of iterated polynomial: $x^3-2x+1$

Rationalizing the denominator having square roots and cube roots

Recurrence $a_{n}=a_{\lfloor 2n/3\rfloor}+a_{\lfloor n/3\rfloor}$

Sum of $\{n\sqrt{2}\}$

Number of real roots of an iterated quadratic: $x^2-3/2$

Integral Representation of the Dottie Number

How many closed paths with the operations $+1$, $-1$, and $\times 2$?

Does continuity depend on the distance function?

Omega Constant Integral

Geometry Construction Problems

Trig identities analogous to $\tan(\pi/5)+4\sin(\pi/5)=\sqrt{5+2\sqrt{5}}$

Interesting Proofs about Metric Spaces?

Extinction probability in a population with competition