The goal of this course is to help children in the fourth grade of primary school to easily and happily read the original English calculus preparation textbook (Precalculus) and learn French, German, Italian, Spanish, Latin, Greek and mathematics while learning English.
Ask parents and friends to give it a try with your child. If you feel that you don't understand something, please post it in the group, and I will revise it according to everyone's opinions.
Ancient humans had two extremely important inventions: one was a rope and the other was a wheel. Between them there is a very mysterious sprite - right angles (90). It is the most important corner in the history of the development of human civilization.
In fact, the ancient Egyptians knew how to divide a rope into 12 equal parts, and then straighten them according to the ratio of 3, 4, and 5 to form a right triangle. Naturally, you get a right angle.
With right angles, it is easy to get a rectangle and thus calculate the land area with the simplest multiplication. This is actually the beginning of integral thinking.
The ancients were particularly adept at using circles to deal with periodic things in time and space.
For ease of learning, the ancient Greeks stood on the shoulders of their predecessors and abstracted the straightened rope into a straight line, and the wheel into a circle.
From concrete things to abstract concepts, human civilization has taken a big leap.
Today's elementary school students can easily understand: if you divide a circle into 4 equal parts, you can get Cartesian coordinates and 4 right angles.
Ask parents and friends to help children pay special attention to the relationship between these sets of data: 30, 45, 60, 90, 180, 360.
When we understand that knowing circles and angles is extremely important for learning most courses such as mathematics, physics, chemistry, and biomedicine, we should be willing to spend more time memorizing some relevant English words.
First, let's learn the word angle for the word "corner" in the English table. It is actually a French word, derived from the Latin word angulus. Where ang- table "corner", -ulus is masculine refers to a small suffix.
At that time, children in the Roman Empire learned mathematics by focusing on the ang-table "horn".
I believe parents and friends can see that French changes the Latin -ulus to -le.
【英语】angle[ˈæŋɡ(ə)l]n.1. 角；角度
a right angle直角
2. Corners; Corner; Edges
3. Opinions; Opinion; Look at the angle of the problem
to consider all angles of the question考虑这个问题的各方面
The professor angled his report to suit the audience he was speaking to.教授为了适合听众的需要调整了他报告的角度。
拆解:ang+le。
Parents and friends must let their children do it themselves, and use online etymology websites like https://www.etymonline.com/ to check the etymology of key words.
Etymology: angle(n.) "difference in space or direction between intersecting lines", late 14th century, from the Old French angle "a corner" (12th century) and directly from the Latin angulus "a corner", is a reduced form from the PIE root *ang-/*ank- "to bend" (the source also includes the Greek ankylos "to bend, to bend", and the Latin ang(u)ere to "compress in bending, folding, strangle"; Old Church Slavic aglu "corner"; Lithuanian anka "ring"; Sanskrit ankah "hook, bend", angam "limb"; Old English ancleo "ankle"; Old High German ango "hook").
认识angle（角）的小朋友，再了解tri-表“三”，rec-表“直”，就已经实际上掌握英语单词triangle（三角形），rectangle（矩形）。
It is important to note that finding the area of a rectangle is the basis for finding the area of all shapes. This is an important foundation for calculus thinking.
请家长朋友帮助孩子大概了解:: 英语的"right angle",对应法语的"angle droit",德语的"right angle",意大利语的"angolo retto",西班牙语的"ángulo recto",日语的"直角(日语罗马字Chokkaku)",希腊语的"ορθή γωνία(拉丁语改写orthí gonía)",意思是"直角"。
Earlier, I emphasized that the ancients were particularly good at using circles to deal with periodic things in time and space.
Therefore, parents and friends must be patient to help children memorize through more contact: circ-, which is derived from Latin, corresponds to cycl-, which is derived from Greek, and the table "circle, period".
【English】circle['sɜːkl]n. circle, loop, social circlev. surround, surround; hovering, rotating; Spread; Circular
拆解:circ+le。
Earlier, we already introduced that the French language changes the Latin -ulus to -le. Thinking backwards, it is easy to deduce that the Latin word for "circle" is circulus.
Circus['sɜːkəs]n. circus, arena, circus
拆解:circ+us。
【English】circum-[ˈsɜːkəm]comb. It means "around, in... around".
拆解:circ+um。
If you know that -ence is a French suffix, and you also know the English word difference, you already have an actual grasp of the English word circumference.
It is highly recommended that parents and friends help their children to understand circumference at least when reading the original English textbook.
【英语】circumference[sɜːˈkʌmfərəns]n.1. 圆周2. 周线；外围；周围
The earth's circumference is more than 40000 kilometres.
The circumference of the Earth is more than 40,000 kilometers.
The lake is twenty miles in circumference.
Twenty miles around the lake.
拆解：circum+fer+ence。
cycle['saɪkl]n. cycle; Bicycle; Loop v. Circulate; cycling; Cycle; Make the cycle; Make the rotation
拆解:cycl+e。
认识cycl-，再记忆英语单词bicycle（自行车），tricycle（三轮车），recycle（再循环）。
There are at least 172 words in English that use circ-, which are basically derived from Latin.
There are at least 213 words in English that use cycl-, which are basically derived from Greek.