Seeking interesting mathematics stories

Seeking interesting mathematics stories

Interesting math story (real!)
Can't include questions

In ancient India, an eminent monk was very proficient in chess, and the king also liked playing chess. One day, the king called the eminent monk to the palace to play chess with him. The king said to him, "I heard that you are very proficient in chess, so I invite you to play chess with me. Don't just because I am the king

Find the range of function f (x) = 1 + X21 − x2

F (x) = 1 + X21 − x2 = - 1 + 21 − X2, ∵ 1-x2 ≤ 1, ∵ 21 − x2 ≥ 2 or 21 − x2 < 0, ∪ - 1 + 21 − x2 ≥ 1 or - 1 + 21 − x2 < - 1, that is, the value range of function f (x) = 1 + X21 − X2 is (- ∞, - 1) ∪ [1, + ∞)

A 1m wide straight path was built on a lawn with length a and width B. now, change this path into a 1m wide curved path to find the remaining lawn area
I know how to ask

Remaining turf area = ab-b
The curved road is equal to the straight road in area
In junior high school, can only use cut fill method. Know it

Clever calculation: [1 + 2 / 1] * [1 + 3 / 1] * [1 + 4 / 1] * * [1 + 8 / 1] * [1 + 9 / 1] * [1 + 10 / 1]

[1 + 2 / 1] * [1 + 3 / 1] * [1 + 4 / 1] * * [1 + 8 / 1] * [1 + 9 / 1] * [1 + 10 / 1]
=3/2*4/3*5/4*.*11/10
Share each other
=11/2
11 out of 2

In the sequence {an}, A1 = 2 / 3 and for any n belonging to N +, there is a (n + 1) = 2A (n) / a (n) + 1
Prove: {1 / a (n) - 1} is an equal ratio sequence

a(n+1)=2a(n)/[a(n)+1 ]
Reciprocal:
1/a(n+1=1/2 +1/[2a(n)]
∴1/a(n+1) -1=1/2·[1/a(n) -1]
{1 / a (n) - 1} is an equal ratio sequence with a common ratio of 0.5, and the first term 1 / A1 - 1 = 1 / 2
1/a(n) -1=1/2^n
a(n)=(2^n)/[1+2^n]

It takes 600 bricks to pave the floor of a classroom with 0.09 square meters of square bricks. If we use square bricks with 0.4 meters of side length to pave the floor, how many do we need?

0.09x600 = 54 (M2)
54 divided by (0.4x0.4) = 337.5 (blocks)
Round it up to 338
Can you reply

Lyrics of 56 nationalities and 56 flowers

Love China
Love China
Hello hello hello hello hello hello
56 constellations 56 flowers
Fifty six brothers and sisters are one family
Fifty six languages in one sentence
Love me China love me China love me China
Love China
Jin's rising pace
Love China
Building our country
Love China
China is magnificent
Love China
Brothers and sisters of 56 ethnic groups
Fifty six languages in one sentence
Love China
Hey, lo

sin²π/8 -cos²π/8

sin²(π/8) -cos²(π/8)
=-cos(2*π/8)
=-cos(π/4)
=-√2/2

As shown in the figure, in the acute angle △ ABC, ab = 10, BC = 11, s △ ABC = 33, find the value of Tanc

Let a be ad ⊥ BC at point D. ∵ s △ ABC = 12bc · ad = 33, ∵ 12 × 11 × ad = 33, ∵ ad = 6. And ∵ AB = 10, ∵ BD = AB2 − ad2 = 102 − 62 = 8. ∵ CD = 11-8 = 3. In RT △ ADC, ∵ Tanc = ADDC = 63 = 2