Who says toys are just "tools for play"?
It can also open people's minds
On the one hand, toys are often derived from life applications
On the other hand, people can also get inspiration from toys
Make further inventions to change lives
Today's article is introduced for everyone
Ancient Chinese toys related to mathematics and physics
You can learn about these toys in the process
Appreciate the profundity of ancient Chinese civilization
Hua Rong Dao
Find the best solution
Cao Cao's defeat at Huarong Dao is a famous Story of the Three Kingdoms
It tells the story of Cao Cao being defeated by Liu Bei and Sun Quan in the Battle of Chibi
While escaping, he passed through Huarong Road and encountered Zhuge Liang's ambush troops
In order to repay Cao Cao's kindness, Guan Yu helped him escape from Huarong Dao
The resulting game - Huarong Road
On Huarong Dao's chessboard, Cao Cao occupies 4 tiles; Guan Yu, Zhang Fei, Zhao Yun, Ma Chao, and Huang Zhong each occupy 2 tiles; and the four soldiers each occupy 1 tile. In the process, only the space left by the two spaces on the board can be used to move the pieces to help Cao Cao move to the bottom middle of the board to escape.
Huarong Road has dozens of deployment methods
Such as "horizontal knife immediately", "close at hand", "through five levels",
"Water leaks", "Little swallow out of the nest" and so on
Many arrangement methods can derive complex chess games
And many players after the proficient game
It was no longer limited to helping "Cao Cao" escape from Huarong Dao
Instead, consider how to escape with the fewest number of steps
So, this involves complex mathematical calculations
In 1952, Chinese mathematician Xu Yuanfang wrote in "Mathematics Talk"
Careful research has been done on Huarong Road games
He continued to explore on the basis of experimentation
The law and reconciliation method of Huarong Dao are summarized, which can be summarized as:
The four creeps cannot be separated, and must be combined in pairs
Guan Yu, Cao Cao and other generals were in the process of moving
Two creeps are needed to open the way ahead
Once Cao Cao moved, there must be two pursuing creeps behind him
Later, through the efforts of masters from all over the world
The number of game solution steps is gradually decreasing
March 1964 by American lawyer Thomas Lyman
A new solution to the classic layout "horizontal knife immediately" was obtained
81 steps can succeed, which is also the best solution known
Now the slider game common on our mobile phones
Most of it is the evolution of Huarong Road
Nine consecutive
Recursive calculation
The Nine Rings are nine rings made of metal wire
The ring is set on a horizontal plate or various frames, and the ring handle is inserted
Its main body is nine rings, one set at a time
It is also worn on the sword-shaped ring handle
The two ends of the ring handle are the handle handle and the handle bar
Zhuo Wenjun during the Western Han Dynasty liked to dismantle the Nine Links
In her letter to her husband Sima Xiangru, she said:
"After parting, the two places hang each other,
It is only said that it is March or April, and who knows five or six years.
The seven-stringed piano has no intention of playing, and the eight-line book cannot be passed on,
Nine consecutive rings were broken from it, and the ten-mile long pavilion was eager to penetrate.
A hundred thoughts, a thousand thoughts, and all kinds of helplessness to resent the king. ”
"Dream of the Red Chamber" also has a description of Lin Daiyu dismantling the nine links
When the Zhou Rui family gave the last two palace flowers to Daiyu, the original text had such a text: "Who knows that at this time, Dai Yu is not in his room, but in the Baoyu room, everyone is stubborn." ”
Each of the nine chains is tied to each other
There are two dismantling rules:
The 1st ring can be placed on or removed at any time; to disassemble the Nth ring (N > 1), the N-1 ring must be placed on the stalk,
And the 1st to N-2 rings are all removed;
The actual process is a mathematical recursive algorithm
Suppose the number of rings is n, and the number of steps to solve each ring is an
The total number of steps required to unlock the n-ring is Sn
According to the disassembly rules, it can be deduced that:
To remove the nth ring, you need to remove the first n-2 rings first
The total number of steps is Sn-2
At this point, another step is required to undo the nth ring
And to understand the nth-1th ring
It is also necessary to put the front n-2 rings on
The first n-2 rings require Sn-2 steps
So removing the nth ring requires an=2Sn-2+1 step
1
2
3
4
5
6
7
8
9
an
11
21
43
85
171
sn
10
42
170
341
therefore
The number of steps required to unlock the nine chains is a sequence of questions:
Known S1=1, S2=2, an=2Sn-2+1, Sn(n≥3)
When n=9, S9=341, i.e. 341 steps are eventually required
Luban lock
Tenon and tenon structure
Luban lock is also known as "Kong Ming lock", "Mo NaiHe", "difficult wood"
Legend has it that it was created by the carpenter's grandfather Lu Ban
Without the use of nails or ropes
Cross and fix the wooden strips by biting
The most common Luban lock consists of six sticks
Each pair of sticks crosses vertically with the other two pairs
The Luban lock is very similar to the mortise and tenon structure of ancient Chinese architecture
Thousands of years ago, building houses was not reinforced concrete, but pure wood
Two separate pieces of wood are fixed together
You have to make them bulges and grooves
In this way, the bumps can be bitten on opposite
At the same time, in order to be able to withstand forces from different directions
The orientation and position of the card slots are also different
This allows the wood to bite together in different dimensions
It's "mortise."
Chinese Heritage, March 2017
The tenon in the vertical direction is called the pin tenon or sleeve top mortise
Inserted into the sea eye or through the eye of the column to ensure stability
Mantou mortises are often made on the stigma to jam the upper component
And in the horizontal direction
Cross-mortise where the crosses intersect so that the members are at the same horizontal line
Tenons are indispensable in traditional Chinese architecture
From the arches of the hall to the handles of the furniture
Layers of overlapping mechanisms look like bricks
But not a single brick or stone was used
Only through the mortise and tenon through the more or less wood
A clever combination between high and low, long and short
Effectively limit the twisting of wood in all directions
It plays a jointing and fixing role
Ancients Cloud: "Ten Thousand Years prison"
In the documentary "The Secrets of the Forbidden City"
The carpenters built a structure in a ratio of 1:5 in tenons and bucket arches
A miniature model of the Forbidden City was copied
In responses to earthquake simulations
There is a slight shaking of the entire mortise and tenon structure model
The energy from the earthquake was consumed between the shaking
This greatly reduces the seismic load of the entire house
It plays a role in earthquake resistance
Tangram
The mystery of the Pythagorean theorem
Tangram boards, as the name suggests, consist of seven blocks
Its history can be traced back to the Pre-Qin Period's Zhou Ji Shu Jing
The Pythagorean theorem is described in it and proved by it
The large square is a pair of tangrams
Two of the large triangles can be put together into a small square
The other 5 pieces can be put together into a small square
Connect the sides of the three squares in two
The formula of a^2 + b^2 = c^2 is shown by these two tangrams
Chinese Heritage, 2009.12
In the Song Dynasty, there was a man named Huang Bosi who invented a set
What began was six small rectangular tables that were later added to seven pieces
I also created some graphics that grouped these small tables together
These graphs can vary according to the number of guests and needs
Tables can be put together into different shapes
He called this small table "Yan Ji"
Later, Ge Shan of the Ming Dynasty described it in his "Butterfly Genealogy"
A small set of thirteen-piece tables
They come in six size shapes, in the form of triangles and trapezoids
These small tables are called butterfly tables
Because they are shaped like butterfly wings
During the Qing Dynasty
Tangram shapes are used in daily necessities, such as Tangram plates
It is usually placed in a wooden box in squares
It can be used to hold dried fruits and desserts during the New Year festival
The porcelain capital of Jingdezhen has fired many types of Tangram plates
Among the many studies, the earliest and most famous questions are:
How many different convex polygons can be spelled out with a pair of tangrams?
The inner angle and polygons up to 180 degrees, i.e. polygons that are convex on all sides
The two Chinese scholars, Wang Fuchun and Xiang Quanqi, solved this problem
In 1942, they came up with the final answer
Among them, there are 1 kind of convex triangle and 6 kinds of convex quadrilateral
There are 2 kinds of convex pentagons and 4 kinds of convex hexagons
Drink water birds
Thermal rationale
Drinking water birds have appeared as early as the Ming Dynasty in China
It is shaped like a bird and the body is made of glass
The body is a glass tube
At the top of the tube is a small ball that is the head of the bird
At the lower end is a large ball containing a volatile liquid of ether, the bird's tail
Dip the beak of the bird into the water and take a sip
After that, the bird will automatically lean down and tirelessly
Repeat the "lean over – get up" drinking process all the time
In fact, the design of the "drinking bird" is implicit
The thermal principle of physics
The heat machine produces mechanical movement through the temperature difference and thus does external work
When starting, drop a little water on the cloth of the bird's head
Water absorbs a lot of heat when it evaporates
Reduce the temperature and air pressure of the bird's head part
And because the temperature decreases, the ether vapor becomes supersaturated
A small amount of ether vapor condenses into a liquid
The amount of steam becomes smaller and the gas volume is further reduced
And exothermic prevents the temperature from dropping
At this point, the air pressure in the lower ball is greater than the air pressure in the upper ball
The temperature difference between the head and tail can be seen under thermal imaging
The ether liquid in the lower ball is pressed upward along the glass tube
The pressure of the lower ball becomes smaller, and the steam inside becomes unsaturated
A small amount of ether vaporizes, and the amount of ether vapor in the lower ball becomes larger
At the same time, the liquid absorbs heat from the ether, so the center of gravity of the whole bird moves up
Thus upsetting the equilibrium
The ether liquid from the lower ball will be pressed against the upper ball
This in turn causes the bird to lean forward and "drink water."
At this point, the lower ball part of the gas enters the upper part
When the two parts of the gas are mixed, the upper and lower pressures are consistent
The liquid will flow back to the lower end under the action of its own gravity
The center of gravity of the drinking bird moved down again, and gradually stood upright
At the same time, the head began to cool again due to the water that had just been soaked
That's it
The bird's head is constantly wet with water, constantly creating a pressure difference
Drinking birds will keep drinking water
The principle is to transfer heat energy through gasification and liquefaction
Today's jet engines, piston engines, etc
All stem from this physical phenomenon
Bamboo dragonfly
Simple helicopter
Bamboo dragonfly is a major invention in ancient China
Rub your hands together, let go of them immediately and you'll fly into the sky
Legend has it that in 400 BC, Chinese began to play with bamboo dragonflies
However, its written records are only in the Ming Dynasty
Seemingly simple bamboo chips and bamboo sticks
But it is the prototype of the birth of the helicopter
The "blades" of the bamboo dragonfly are rounded in front and sharp in the back
The upper surface is slightly rounded and the lower surface is straight
When the hand rubs the bamboo stick to drive the blades to rotate
As air flows through the upper surface
Due to the arc of the arch, the flow rate is fast but the pressure is small
The lower surface is slow but under high pressure due to the flat DC speed
A pressure difference is thus formed between the upper and lower surfaces
An upward lift is generated
As the blades turn faster and faster, when the lift is greater than the gravity of the bamboo dragonfly
It will take off
In the middle of the 15th century, bamboo dragonflies spread to Europe
Known as the "China Spiral"
Leonardo da Vinci took inspiration from it
Draw the ideal helicopter drawing
And hundreds of years later, it has been continuously tested and improved by future generations
A real helicopter was born
Although the helicopter is a million times more complicated than the bamboo dragonfly
But the principle of flight is the same as the rotor is the blade of the bamboo dragonfly
The rotor shaft is the bamboo stick of the bamboo dragonfly
The engine that drives the rotor is the hands of the bamboo sticks
Chinese toy culture has a long history
Whether it's seasonal toys, educational toys, or observation toys
All of them have made the creative spirit of ancient Chinese constantly evolve
And use this as a mirror
Reflect our true disposition in their daily lives
bibliography:
Chinese Old Toys: Applied Science. Naturalist 2015.06
Mortise: "Spell" out of the world . Chinese Heritage 2017.03
topic
See you in the message area
- END -
Edit | Yin Shi painting
Image source | Internet
Geography Junior Classroom May | April | March | February | January 2020
December | November | October 2019
The correct way to open spring is to eat spring vegetables
Fibonacci Sequence: The Beauty of Mathematics Hidden in Nature