geometric mean的音標為[d?i??metr?k mi?n]，基本翻譯為“幾何平均數”，速記技巧為“幾何均數，幾何圖形求平均”。

Geometric mean 的英文詞源可以追溯到古希臘數學家歐幾里得（Euclid），他提出了幾何學的定義和基礎理論。

Geometric mean 的變化形式主要有復數形式 geometric means，以及其比較級和最高級形式 geometric mean, geometric meanst, geometric meansthe most。

相關單詞有：

magnitude：意為大小或量度，與 geometric mean 有一定的關聯，表示幾何的數量或規模。

arithmetic：意為算術的，與幾何學無關，但可以表示計算或運算的過程。

geometrical：意為幾何的，與幾何學相關，常用于描述幾何形狀或性質。

dimension：意為維度或尺寸，與幾何學中的維度概念有關。

curvature：意為曲率或彎曲程度，與幾何學中的曲線形狀有關。

perspective：意為透視圖或視角，與幾何學中的透視原理有關。

conic section：意為圓錐截面或圓錐曲線，與幾何學中的圓錐形狀有關。

plane geometry：意為平面幾何學，是幾何學的基礎課程之一。

solid geometry：意為立體幾何學，是幾何學的延伸課程之一。

以上單詞都與幾何學相關，并可以用來描述幾何學中的概念和性質。

常用短語：

1. geometric growth 幾何增長

2. geometric mean 幾何平均數

3. geometric progression 等比數列

4. geometric series 幾何級數

5. geometric mean of numbers 數字的幾何平均數

6. geometric mean of ratios 比率的幾何平均數

7. geometric average 幾何平均值

例句：

1. The company"s revenue has been growing at a geometric rate of 20% per year.

2. The geometric mean of the scores on the exam was 75%.

3. The geometric series adds up to infinity, but its mean value approaches a limit.

4. The geometric mean of the numbers in the equation is 1/x.

5. The geometric mean of the ratios in the table is 0.75.

6. The geometric average of the numbers in the column is 3.

7. The company"s profits have increased geometrically over the past few years.

英文小作文：

The geometric mean is a mathematical concept that measures the average value of a set of numbers or ratios. It is a way of taking into account all values in a set and calculating a single number that represents their overall average. In practical terms, the geometric mean can be used to calculate averages of measurements that are not normally distributed, but have a certain degree of variability and growth potential.

For example, consider a company that is growing its revenues and profits at a geometric rate of 20% per year. If we calculate the geometric mean of these growth rates, we can see how all of the revenues and profits are contributing to a larger overall value, even though some may be larger than others at any given time. Similarly, in a financial context, the geometric mean can be used to calculate the overall value of a portfolio or investment strategy, taking into account the growth potential of each asset or investment.

In summary, the geometric mean is a useful tool for understanding and analyzing data sets that have variability and growth potential, and it can be applied to various contexts, from business growth to financial analysis.