diff --git a/library/math.po b/library/math.po
index e5df4b088c..37fdeb724b 100644
--- a/library/math.po
+++ b/library/math.po
@@ -70,7 +70,7 @@ msgstr ":func:`factorial(n) <factorial>`"
 
 #: ../../library/math.rst:33
 msgid "*n* factorial"
-msgstr ""
+msgstr "*n* 的階乘"
 
 #: ../../library/math.rst:34
 msgid ":func:`gcd(*integers) <gcd>`"
@@ -78,7 +78,7 @@ msgstr ":func:`gcd(*integers) <gcd>`"
 
 #: ../../library/math.rst:34
 msgid "Greatest common divisor of the integer arguments"
-msgstr ""
+msgstr "整數引數的最大公因數"
 
 #: ../../library/math.rst:35
 msgid ":func:`isqrt(n) <isqrt>`"
@@ -86,7 +86,7 @@ msgstr ":func:`isqrt(n) <isqrt>`"
 
 #: ../../library/math.rst:35
 msgid "Integer square root of a nonnegative integer *n*"
-msgstr ""
+msgstr "非負整數 *n* 的整數平方根"
 
 #: ../../library/math.rst:36
 msgid ":func:`lcm(*integers) <lcm>`"
@@ -94,7 +94,7 @@ msgstr ":func:`lcm(*integers) <lcm>`"
 
 #: ../../library/math.rst:36
 msgid "Least common multiple of the integer arguments"
-msgstr ""
+msgstr "整數引數的最小公倍數"
 
 #: ../../library/math.rst:37
 msgid ":func:`perm(n, k) <perm>`"
@@ -108,7 +108,7 @@ msgstr "從 *n* 個物品中不重複但考慮排序地取出 *k* 個物品的
 
 #: ../../library/math.rst:39
 msgid "**Floating point arithmetic**"
-msgstr ""
+msgstr "**浮點數算術運算**"
 
 #: ../../library/math.rst:41
 msgid ":func:`ceil(x) <ceil>`"
@@ -116,7 +116,7 @@ msgstr ":func:`ceil(x) <ceil>`"
 
 #: ../../library/math.rst:41
 msgid "Ceiling of *x*, the smallest integer greater than or equal to *x*"
-msgstr ""
+msgstr "*x* 的上取整值，即大於或等於 *x* 的最小整數"
 
 #: ../../library/math.rst:42
 msgid ":func:`fabs(x) <fabs>`"
@@ -132,7 +132,7 @@ msgstr ":func:`floor(x)  <floor>`"
 
 #: ../../library/math.rst:43
 msgid "Floor of *x*, the largest integer less than or equal to *x*"
-msgstr ""
+msgstr "*x* 的下取整值，即小於或等於 *x* 的最大整數"
 
 #: ../../library/math.rst:44
 msgid ":func:`fma(x, y, z) <fma>`"
@@ -140,7 +140,7 @@ msgstr ":func:`fma(x, y, z) <fma>`"
 
 #: ../../library/math.rst:44
 msgid "Fused multiply-add operation: ``(x * y) + z``"
-msgstr ""
+msgstr "融合乘加運算：``(x * y) + z``"
 
 #: ../../library/math.rst:45
 msgid ":func:`fmod(x, y) <fmod>`"
@@ -148,7 +148,7 @@ msgstr ":func:`fmod(x, y) <fmod>`"
 
 #: ../../library/math.rst:45
 msgid "Remainder of division ``x / y``"
-msgstr ""
+msgstr "除法 ``x / y`` 的餘數"
 
 #: ../../library/math.rst:46
 msgid ":func:`modf(x) <modf>`"
@@ -156,7 +156,7 @@ msgstr ":func:`modf(x) <modf>`"
 
 #: ../../library/math.rst:46
 msgid "Fractional and integer parts of *x*"
-msgstr ""
+msgstr "*x* 的小數部分與整數部分"
 
 #: ../../library/math.rst:47
 msgid ":func:`remainder(x, y) <remainder>`"
@@ -164,7 +164,7 @@ msgstr ":func:`remainder(x, y) <remainder>`"
 
 #: ../../library/math.rst:47
 msgid "Remainder of *x* with respect to *y*"
-msgstr ""
+msgstr "*x* 相對於 *y* 的餘數"
 
 #: ../../library/math.rst:48
 msgid ":func:`trunc(x) <trunc>`"
@@ -172,7 +172,7 @@ msgstr ":func:`trunc(x) <trunc>`"
 
 #: ../../library/math.rst:48
 msgid "Integer part of *x*"
-msgstr ""
+msgstr "*x* 的整數部分"
 
 #: ../../library/math.rst:50
 msgid "**Floating point manipulation functions**"
@@ -184,7 +184,7 @@ msgstr ":func:`copysign(x, y) <copysign>`"
 
 #: ../../library/math.rst:52
 msgid "Magnitude (absolute value) of *x* with the sign of *y*"
-msgstr ""
+msgstr "帶有 *y* 的正負號的 *x* 的量值（絕對值）"
 
 #: ../../library/math.rst:53
 msgid ":func:`frexp(x) <frexp>`"
@@ -192,7 +192,7 @@ msgstr ":func:`frexp(x) <frexp>`"
 
 #: ../../library/math.rst:53
 msgid "Mantissa and exponent of *x*"
-msgstr ""
+msgstr "*x* 的尾數與指數"
 
 #: ../../library/math.rst:54
 msgid ":func:`isclose(a, b, rel_tol, abs_tol) <isclose>`"
@@ -200,7 +200,7 @@ msgstr ":func:`isclose(a, b, rel_tol, abs_tol) <isclose>`"
 
 #: ../../library/math.rst:54
 msgid "Check if the values *a* and *b* are close to each other"
-msgstr ""
+msgstr "檢查 *a* 與 *b* 兩值是否足夠接近"
 
 #: ../../library/math.rst:55
 msgid ":func:`isfinite(x) <isfinite>`"
@@ -208,7 +208,7 @@ msgstr ":func:`isfinite(x) <isfinite>`"
 
 #: ../../library/math.rst:55
 msgid "Check if *x* is neither an infinity nor a NaN"
-msgstr ""
+msgstr "檢查 *x* 是否既非無限值也非 NaN"
 
 #: ../../library/math.rst:56
 msgid ":func:`isinf(x) <isinf>`"
@@ -216,7 +216,7 @@ msgstr ":func:`isinf(x) <isinf>`"
 
 #: ../../library/math.rst:56
 msgid "Check if *x* is a positive or negative infinity"
-msgstr ""
+msgstr "檢查 *x* 是否為正無限或負無限"
 
 #: ../../library/math.rst:57
 msgid ":func:`isnan(x) <isnan>`"
@@ -224,7 +224,7 @@ msgstr ":func:`isnan(x) <isnan>`"
 
 #: ../../library/math.rst:57
 msgid "Check if *x* is a NaN  (not a number)"
-msgstr ""
+msgstr "檢查 *x* 是否為 NaN（非數值）"
 
 #: ../../library/math.rst:58
 msgid ":func:`ldexp(x, i) <ldexp>`"
@@ -232,7 +232,7 @@ msgstr ":func:`ldexp(x, i) <ldexp>`"
 
 #: ../../library/math.rst:58
 msgid "``x * (2**i)``, inverse of function :func:`frexp`"
-msgstr ""
+msgstr "``x * (2**i)``，:func:`frexp` 的反函式"
 
 #: ../../library/math.rst:59
 msgid ":func:`nextafter(x, y, steps) <nextafter>`"
@@ -240,7 +240,7 @@ msgstr ":func:`nextafter(x, y, steps) <nextafter>`"
 
 #: ../../library/math.rst:59
 msgid "Floating-point value *steps* steps after *x* towards *y*"
-msgstr ""
+msgstr "從 *x* 向 *y* 移動 *steps* 步的浮點數值"
 
 #: ../../library/math.rst:60
 msgid ":func:`ulp(x) <ulp>`"
@@ -248,11 +248,11 @@ msgstr ":func:`ulp(x) <ulp>`"
 
 #: ../../library/math.rst:60
 msgid "Value of the least significant bit of *x*"
-msgstr ""
+msgstr "*x* 的最低有效位元的值"
 
 #: ../../library/math.rst:62
 msgid "**Power, exponential and logarithmic functions**"
-msgstr ""
+msgstr "**次方、指數與對數函式**"
 
 #: ../../library/math.rst:64
 msgid ":func:`cbrt(x) <cbrt>`"
@@ -260,7 +260,7 @@ msgstr ":func:`cbrt(x) <cbrt>`"
 
 #: ../../library/math.rst:64
 msgid "Cube root of *x*"
-msgstr ""
+msgstr "*x* 的立方根"
 
 #: ../../library/math.rst:65
 msgid ":func:`exp(x) <exp>`"
@@ -268,7 +268,7 @@ msgstr ":func:`exp(x) <exp>`"
 
 #: ../../library/math.rst:65
 msgid "*e* raised to the power *x*"
-msgstr ""
+msgstr "*e* 的 *x* 次方"
 
 #: ../../library/math.rst:66
 msgid ":func:`exp2(x) <exp2>`"
@@ -276,7 +276,7 @@ msgstr ":func:`exp2(x) <exp2>`"
 
 #: ../../library/math.rst:66
 msgid "*2* raised to the power *x*"
-msgstr ""
+msgstr "*2* 的 *x* 次方"
 
 #: ../../library/math.rst:67
 msgid ":func:`expm1(x) <expm1>`"
@@ -284,7 +284,7 @@ msgstr ":func:`expm1(x) <expm1>`"
 
 #: ../../library/math.rst:67
 msgid "*e* raised to the power *x*, minus 1"
-msgstr ""
+msgstr "*e* 的 *x* 次方減 1"
 
 #: ../../library/math.rst:68
 msgid ":func:`log(x, base) <log>`"
@@ -292,7 +292,7 @@ msgstr ":func:`log(x, base) <log>`"
 
 #: ../../library/math.rst:68
 msgid "Logarithm of *x* to the given base (*e* by default)"
-msgstr ""
+msgstr "*x* 以給定底數（預設為 *e*）的對數"
 
 #: ../../library/math.rst:69
 msgid ":func:`log1p(x) <log1p>`"
@@ -300,7 +300,7 @@ msgstr ":func:`log1p(x) <log1p>`"
 
 #: ../../library/math.rst:69
 msgid "Natural logarithm of *1+x* (base *e*)"
-msgstr ""
+msgstr "*1+x* 的自然對數（以 *e* 為底）"
 
 #: ../../library/math.rst:70
 msgid ":func:`log2(x) <log2>`"
@@ -308,7 +308,7 @@ msgstr ":func:`log2(x) <log2>`"
 
 #: ../../library/math.rst:70
 msgid "Base-2 logarithm of *x*"
-msgstr ""
+msgstr "*x* 的以 2 為底的對數"
 
 #: ../../library/math.rst:71
 msgid ":func:`log10(x) <log10>`"
@@ -316,7 +316,7 @@ msgstr ":func:`log10(x) <log10>`"
 
 #: ../../library/math.rst:71
 msgid "Base-10 logarithm of *x*"
-msgstr ""
+msgstr "*x* 的以 10 為底的對數"
 
 #: ../../library/math.rst:72
 msgid ":func:`pow(x, y) <math.pow>`"
@@ -324,7 +324,7 @@ msgstr ":func:`pow(x, y) <math.pow>`"
 
 #: ../../library/math.rst:72
 msgid "*x* raised to the power *y*"
-msgstr ""
+msgstr "*x* 的 *y* 次方"
 
 #: ../../library/math.rst:73
 msgid ":func:`sqrt(x) <sqrt>`"
@@ -336,7 +336,7 @@ msgstr "*x* 的平方根"
 
 #: ../../library/math.rst:75
 msgid "**Summation and product functions**"
-msgstr ""
+msgstr "**總和與乘積函式**"
 
 #: ../../library/math.rst:77
 msgid ":func:`dist(p, q) <dist>`"
@@ -346,7 +346,7 @@ msgstr ":func:`dist(p, q) <dist>`"
 msgid ""
 "Euclidean distance between two points *p* and *q* given as an iterable of "
 "coordinates"
-msgstr ""
+msgstr "兩點 *p* 與 *q* 之間的歐幾里得距離，各點以座標的可疊代物件表示"
 
 #: ../../library/math.rst:78
 msgid ":func:`fsum(iterable) <fsum>`"
@@ -354,7 +354,7 @@ msgstr ":func:`fsum(iterable) <fsum>`"
 
 #: ../../library/math.rst:78
 msgid "Sum of values in the input *iterable*"
-msgstr ""
+msgstr "輸入 *iterable* 中所有值的總和"
 
 #: ../../library/math.rst:79
 msgid ":func:`hypot(*coordinates) <hypot>`"
@@ -362,7 +362,7 @@ msgstr ":func:`hypot(*coordinates) <hypot>`"
 
 #: ../../library/math.rst:79
 msgid "Euclidean norm of an iterable of coordinates"
-msgstr ""
+msgstr "座標可疊代物件的歐幾里得範數"
 
 #: ../../library/math.rst:80
 msgid ":func:`prod(iterable, start) <prod>`"
@@ -370,7 +370,7 @@ msgstr ":func:`prod(iterable, start) <prod>`"
 
 #: ../../library/math.rst:80
 msgid "Product of elements in the input *iterable* with a *start* value"
-msgstr ""
+msgstr "輸入 *iterable* 中所有元素與 *start* 起始值的乘積"
 
 #: ../../library/math.rst:81
 msgid ":func:`sumprod(p, q) <sumprod>`"
@@ -378,11 +378,11 @@ msgstr ":func:`sumprod(p, q) <sumprod>`"
 
 #: ../../library/math.rst:81
 msgid "Sum of products from two iterables *p* and *q*"
-msgstr ""
+msgstr "兩個可疊代物件 *p* 與 *q* 各元素乘積的總和"
 
 #: ../../library/math.rst:83
 msgid "**Angular conversion**"
-msgstr ""
+msgstr "**角度轉換**"
 
 #: ../../library/math.rst:85
 msgid ":func:`degrees(x) <degrees>`"
@@ -390,7 +390,7 @@ msgstr ":func:`degrees(x) <degrees>`"
 
 #: ../../library/math.rst:85
 msgid "Convert angle *x* from radians to degrees"
-msgstr ""
+msgstr "將角度 *x* 從弧度轉換為度"
 
 #: ../../library/math.rst:86
 msgid ":func:`radians(x) <radians>`"
@@ -398,11 +398,11 @@ msgstr ":func:`radians(x) <radians>`"
 
 #: ../../library/math.rst:86
 msgid "Convert angle *x* from degrees to radians"
-msgstr ""
+msgstr "將角度 *x* 從度轉換為弧度"
 
 #: ../../library/math.rst:88
 msgid "**Trigonometric functions**"
-msgstr ""
+msgstr "**三角函式**"
 
 #: ../../library/math.rst:90
 msgid ":func:`acos(x) <acos>`"
@@ -410,7 +410,7 @@ msgstr ":func:`acos(x) <acos>`"
 
 #: ../../library/math.rst:90
 msgid "Arc cosine of *x*"
-msgstr ""
+msgstr "*x* 的反餘弦"
 
 #: ../../library/math.rst:91
 msgid ":func:`asin(x) <asin>`"
@@ -418,7 +418,7 @@ msgstr ":func:`asin(x) <asin>`"
 
 #: ../../library/math.rst:91
 msgid "Arc sine of *x*"
-msgstr ""
+msgstr "*x* 的反正弦"
 
 #: ../../library/math.rst:92
 msgid ":func:`atan(x) <atan>`"
@@ -426,7 +426,7 @@ msgstr ":func:`atan(x) <atan>`"
 
 #: ../../library/math.rst:92
 msgid "Arc tangent of *x*"
-msgstr ""
+msgstr "*x* 的反正切"
 
 #: ../../library/math.rst:93
 msgid ":func:`atan2(y, x) <atan2>`"
@@ -442,7 +442,7 @@ msgstr ":func:`cos(x) <cos>`"
 
 #: ../../library/math.rst:94
 msgid "Cosine of *x*"
-msgstr ""
+msgstr "*x* 的餘弦"
 
 #: ../../library/math.rst:95
 msgid ":func:`sin(x) <sin>`"
@@ -450,7 +450,7 @@ msgstr ":func:`sin(x) <sin>`"
 
 #: ../../library/math.rst:95
 msgid "Sine of *x*"
-msgstr ""
+msgstr "*x* 的正弦"
 
 #: ../../library/math.rst:96
 msgid ":func:`tan(x) <tan>`"
@@ -458,11 +458,11 @@ msgstr ":func:`tan(x) <tan>`"
 
 #: ../../library/math.rst:96
 msgid "Tangent of *x*"
-msgstr ""
+msgstr "*x* 的正切"
 
 #: ../../library/math.rst:98
 msgid "**Hyperbolic functions**"
-msgstr ""
+msgstr "**雙曲函式**"
 
 #: ../../library/math.rst:100
 msgid ":func:`acosh(x) <acosh>`"
@@ -470,7 +470,7 @@ msgstr ":func:`acosh(x) <acosh>`"
 
 #: ../../library/math.rst:100
 msgid "Inverse hyperbolic cosine of *x*"
-msgstr ""
+msgstr "*x* 的反雙曲餘弦"
 
 #: ../../library/math.rst:101
 msgid ":func:`asinh(x) <asinh>`"
@@ -478,7 +478,7 @@ msgstr ":func:`asinh(x) <asinh>`"
 
 #: ../../library/math.rst:101
 msgid "Inverse hyperbolic sine of *x*"
-msgstr ""
+msgstr "*x* 的反雙曲正弦"
 
 #: ../../library/math.rst:102
 msgid ":func:`atanh(x) <atanh>`"
@@ -486,7 +486,7 @@ msgstr ":func:`atanh(x) <atanh>`"
 
 #: ../../library/math.rst:102
 msgid "Inverse hyperbolic tangent of *x*"
-msgstr ""
+msgstr "*x* 的反雙曲正切"
 
 #: ../../library/math.rst:103
 msgid ":func:`cosh(x) <cosh>`"
@@ -494,7 +494,7 @@ msgstr ":func:`cosh(x) <cosh>`"
 
 #: ../../library/math.rst:103
 msgid "Hyperbolic cosine of *x*"
-msgstr ""
+msgstr "*x* 的雙曲餘弦"
 
 #: ../../library/math.rst:104
 msgid ":func:`sinh(x) <sinh>`"
@@ -502,7 +502,7 @@ msgstr ":func:`sinh(x) <sinh>`"
 
 #: ../../library/math.rst:104
 msgid "Hyperbolic sine of *x*"
-msgstr ""
+msgstr "*x* 的雙曲正弦"
 
 #: ../../library/math.rst:105
 msgid ":func:`tanh(x) <tanh>`"
@@ -510,11 +510,11 @@ msgstr ":func:`tanh(x) <tanh>`"
 
 #: ../../library/math.rst:105
 msgid "Hyperbolic tangent of *x*"
-msgstr ""
+msgstr "*x* 的雙曲正切"
 
 #: ../../library/math.rst:107
 msgid "**Special functions**"
-msgstr ""
+msgstr "**特殊函式**"
 
 #: ../../library/math.rst:109
 msgid ":func:`erf(x) <erf>`"
@@ -522,7 +522,7 @@ msgstr ":func:`erf(x) <erf>`"
 
 #: ../../library/math.rst:109
 msgid "`Error function <https://en.wikipedia.org/wiki/Error_function>`_ at *x*"
-msgstr ""
+msgstr "在 *x* 處的\\ `誤差函式 <https://en.wikipedia.org/wiki/Error_function>`_\\ 值"
 
 #: ../../library/math.rst:110
 msgid ":func:`erfc(x) <erfc>`"
@@ -533,6 +533,8 @@ msgid ""
 "`Complementary error function <https://en.wikipedia.org/wiki/"
 "Error_function>`_ at *x*"
 msgstr ""
+"在 *x* 處的\\ `互補誤差函式 <https://en.wikipedia.org/wiki/"
+"Error_function>`_\\ 值"
 
 #: ../../library/math.rst:111
 msgid ":func:`gamma(x) <gamma>`"
@@ -540,7 +542,7 @@ msgstr ":func:`gamma(x) <gamma>`"
 
 #: ../../library/math.rst:111
 msgid "`Gamma function <https://en.wikipedia.org/wiki/Gamma_function>`_ at *x*"
-msgstr ""
+msgstr "在 *x* 處的 `Gamma 函式 <https://en.wikipedia.org/wiki/Gamma_function>`_\\ 值"
 
 #: ../../library/math.rst:112
 msgid ":func:`lgamma(x) <lgamma>`"
@@ -551,6 +553,8 @@ msgid ""
 "Natural logarithm of the absolute value of the `Gamma function <https://"
 "en.wikipedia.org/wiki/Gamma_function>`_ at *x*"
 msgstr ""
+"在 *x* 處的 `Gamma 函式 <https://"
+"en.wikipedia.org/wiki/Gamma_function>`_\\ 絕對值的自然對數"
 
 #: ../../library/math.rst:114
 msgid "**Constants**"
@@ -594,7 +598,7 @@ msgstr ":data:`nan`"
 
 #: ../../library/math.rst:120
 msgid "\"Not a number\" (NaN)"
-msgstr ""
+msgstr "「非數值」（NaN）"
 
 #: ../../library/math.rst:125
 msgid "Number-theoretic functions"
@@ -630,7 +634,7 @@ msgstr ""
 
 #: ../../library/math.rst:147
 msgid "Return factorial of the nonnegative integer *n*."
-msgstr ""
+msgstr "回傳非負整數 *n* 的階乘。"
 
 #: ../../library/math.rst:149
 msgid "Floats with integral values (like ``5.0``) are no longer accepted."
@@ -707,8 +711,7 @@ msgstr ""
 
 #: ../../library/math.rst:211
 msgid "Floating point arithmetic"
-msgstr ""
-"計算傳入的 *iterable* 中所有元素的乘積。預設的乘積起始值 *start* 為 ``1``。"
+msgstr "浮點數算術運算"
 
 #: ../../library/math.rst:215
 msgid ""
@@ -741,8 +744,8 @@ msgid ""
 "``float`` format. This operation often provides better accuracy than the "
 "direct expression ``(x * y) + z``."
 msgstr ""
-"融合乘加運算。回傳 ``(x * y) + z``，用近似於無限精度及範圍的方式計算，而後一"
-"次轉換為 ``float`` 格式。此操作通常能提供比運算式 ``(x * y) + z`` 更高的準確度。"
+"融合乘加運算。回傳 ``(x * y) + z``，用近似於無限精密度及範圍的方式計算，而後一"
+"次轉換為 ``float`` 格式。此操作通常能提供比運算式 ``(x * y) + z`` 更高的精確度。"
 
 #: ../../library/math.rst:239
 msgid ""
@@ -773,8 +776,8 @@ msgid ""
 msgstr ""
 "回傳 ``x / y`` 的浮點數餘數，其以平臺上的 C 函式庫 ``fmod(x, y)`` 函式定義。"
 "請注意此函式與 Python 運算式 ``x % y`` 可能不會回傳相同結果。C 標準要求 "
-"``fmod(x, y)`` 的回傳值完全等同（數學定義上，即無限精度）於 ``x - n*y``，*n* "
-"為可使回傳值與 *x* 同號且長度小於 ``abs(y)`` 的整數。Python 運算式 ``x % y`` "
+"``fmod(x, y)`` 的回傳值完全等同（數學定義上，即無限精密度）於 ``x - n*y``，*n*"
+"為可使回傳值與 *x* 同號且量值小於 ``abs(y)`` 的整數。Python 運算式 ``x % y`` "
 "的回傳值則與 *y* 同號，且可能無法精確地計算浮點數引數。例如：``fmod(-1e-100, "
 "1e100)`` 的值為 ``-1e-100``，但 Python 運算式 ``-1e-100 % 1e100`` 的結果為 "
 "``1e100-1e-100``，此值無法準確地表示成浮點數，並會四捨五入為出乎意料的 "
@@ -853,14 +856,14 @@ msgid ""
 "(the same as the platform C double type), in which case any float *x* with "
 "``abs(x) >= 2**52`` necessarily has no fractional bits."
 msgstr ""
-"使用 :func:`ceil`、:func:`floor` 及 :func:`modf` 三個函式時，請注意 *所有* 足"
-"夠大的浮點數都是精確的整數。Python 的浮點數型別的精確度通常不會超過 53 位元"
+"使用 :func:`ceil`、:func:`floor` 及 :func:`modf` 三個函式時，請注意\\ *所有*\\ 足"
+"夠大的浮點數都是精確的整數。Python 的浮點數型別的精密度通常不會超過 53 位元"
 "（與 C 語言 double 型別相同），因此當浮點數 *x* 滿足 ``abs(x) >= 2**52`` 時，"
 "它必然沒有小數部分。"
 
 #: ../../library/math.rst:313
 msgid "Floating point manipulation functions"
-msgstr ""
+msgstr "浮點數操作函式"
 
 #: ../../library/math.rst:317
 msgid ""
@@ -868,7 +871,7 @@ msgid ""
 "*y*.  On platforms that support signed zeros, ``copysign(1.0, -0.0)`` "
 "returns *-1.0*."
 msgstr ""
-"回傳與 *x* 相同長度（絕對值）且與 *y* 同號的浮點數。在支援帶符號零的平臺上，"
+"回傳與 *x* 相同量值（絕對值）且與 *y* 同號的浮點數。在支援帶符號零的平臺上，"
 "``copysign(1.0, -0.0)`` 回傳 *-1.0*。"
 
 #: ../../library/math.rst:324
@@ -930,6 +933,10 @@ msgid ""
 "and *rel_tol* less than ``1.0``.  So add an appropriate positive *abs_tol* "
 "argument to the call."
 msgstr ""
+"*abs_tol* 為絕對容許偏差；預設為 ``0.0`` 且必須不為負。當比較 ``x`` 與 "
+"``0.0`` 時，``isclose(x, 0)`` 將計算為 ``abs(x) <= rel_tol  * abs(x)``，此結果"
+"對任何非零 ``x`` 及小於 ``1.0`` 的 *rel_tol* 而言皆為 ``False``。因此呼叫時應"
+"加上適當的正數 *abs_tol* 引數。"
 
 #: ../../library/math.rst:356
 msgid ""
@@ -1066,7 +1073,7 @@ msgstr ""
 
 #: ../../library/math.rst:440
 msgid "Power, exponential and logarithmic functions"
-msgstr ""
+msgstr "次方、指數與對數函式"
 
 #: ../../library/math.rst:444
 msgid "Return the cube root of *x*."
@@ -1078,6 +1085,8 @@ msgid ""
 "natural logarithms.  This is usually more accurate than ``math.e ** x`` or "
 "``pow(math.e, x)``."
 msgstr ""
+"回傳 *e* 的 *x* 次方，其中 *e* = 2.718281... 為自然對數的底數。此函式通常比 "
+"``math.e ** x`` 或 ``pow(math.e, x)`` 更為精確。"
 
 #: ../../library/math.rst:458
 msgid "Return *2* raised to the power *x*."
@@ -1091,40 +1100,49 @@ msgid ""
 "wiki/Loss_of_significance>`_\\; the :func:`expm1` function provides a way to "
 "compute this quantity to full precision:"
 msgstr ""
+"回傳 *e* 的 *x* 次方減 1。此處 *e* 為自然對數的底數。對於較小的浮點數 *x*，"
+"``exp(x) - 1`` 中的減法運算可能導致\\ `顯著的精密度損失 <https://en.wikipedia.org/"
+"wiki/Loss_of_significance>`_；:func:`expm1` 函式提供了一種能以完整精密度計算此值的方法："
 
 #: ../../library/math.rst:482
 msgid "With one argument, return the natural logarithm of *x* (to base *e*)."
-msgstr ""
+msgstr "傳入一個引數時，回傳 *x* 的自然對數（以 *e* 為底）。"
 
 #: ../../library/math.rst:484
 msgid ""
 "With two arguments, return the logarithm of *x* to the given *base*, "
 "calculated as ``log(x)/log(base)``."
 msgstr ""
+"傳入兩個引數時，回傳 *x* 以給定 *base* 為底的對數，計算方式為 "
+"``log(x)/log(base)``。"
 
 #: ../../library/math.rst:490
 msgid ""
 "Return the natural logarithm of *1+x* (base *e*). The result is calculated "
 "in a way which is accurate for *x* near zero."
 msgstr ""
+"回傳 *1+x* 的自然對數（以 *e* 為底）。計算結果對於接近零的 *x* 值是精確的。"
 
 #: ../../library/math.rst:496
 msgid ""
 "Return the base-2 logarithm of *x*. This is usually more accurate than "
 "``log(x, 2)``."
 msgstr ""
+"回傳 *x* 的以 2 為底的對數。此函式通常比 ``log(x, 2)`` 更為精確。"
 
 #: ../../library/math.rst:503
 msgid ""
 ":meth:`int.bit_length` returns the number of bits necessary to represent an "
 "integer in binary, excluding the sign and leading zeros."
 msgstr ""
+":meth:`int.bit_length` 回傳以二進位表示一個整數所需的位元數，不包含正負號及前導零。"
 
 #: ../../library/math.rst:509
 msgid ""
 "Return the base-10 logarithm of *x*.  This is usually more accurate than "
 "``log(x, 10)``."
 msgstr ""
+"回傳 *x* 的以 10 為底的對數。此函式通常比 ``log(x, 10)`` 更為精確。"
 
 #: ../../library/math.rst:515
 msgid ""
@@ -1134,6 +1152,9 @@ msgid ""
 "and *y* are finite, *x* is negative, and *y* is not an integer then ``pow(x, "
 "y)`` is undefined, and raises :exc:`ValueError`."
 msgstr ""
+"回傳 *x* 的 *y* 次方。例外情況盡可能遵循 IEEE 754 標準。特別是，``pow(1.0, "
+"x)`` 和 ``pow(x, 0.0)`` 總是回傳 ``1.0``，即使 *x* 是零或 NaN 也是如此。若 "
+"*x* 和 *y* 皆為有限數、*x* 為負數且 *y* 不是整數，則 ``pow(x, y)`` 是未定義的，並會引發 :exc:`ValueError`。"
 
 #: ../../library/math.rst:522
 msgid ""
@@ -1141,6 +1162,8 @@ msgid ""
 "arguments to type :class:`float`.  Use ``**`` or the built-in :func:`pow` "
 "function for computing exact integer powers."
 msgstr ""
+"與內建 ``**`` 運算子不同，:func:`math.pow` 會將其兩個引數都轉換為 :class:`float` "
+"型別。若需要計算精確的整數次方，請使用 ``**`` 或內建的 :func:`pow` 函式。"
 
 #: ../../library/math.rst:526
 msgid ""
@@ -1148,6 +1171,8 @@ msgid ""
 "return ``inf`` instead of raising :exc:`ValueError`, for consistency with "
 "IEEE 754."
 msgstr ""
+"特殊情況 ``pow(0.0, -inf)`` 和 ``pow(-0.0, -inf)`` 已變更為回傳 ``inf`` 而非引發 "
+":exc:`ValueError`，以符合 IEEE 754 標準。"
 
 #: ../../library/math.rst:534
 msgid "Return the square root of *x*."
@@ -1155,7 +1180,7 @@ msgstr "回傳 *x* 的平方根。"
 
 #: ../../library/math.rst:538
 msgid "Summation and product functions"
-msgstr ""
+msgstr "總和與乘積函式"
 
 #: ../../library/math.rst:542
 msgid ""
@@ -1163,10 +1188,12 @@ msgid ""
 "a sequence (or iterable) of coordinates.  The two points must have the same "
 "dimension."
 msgstr ""
+"回傳兩點 *p* 與 *q* 之間的歐幾里得距離，各點以座標的序列（或可疊代物件）表示。"
+"兩點必須具有相同的維度。"
 
 #: ../../library/math.rst:546 ../../library/math.rst:607
 msgid "Roughly equivalent to::"
-msgstr "約等價於：::"
+msgstr "約等價於： ::"
 
 #: ../../library/math.rst:548
 msgid "sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q)))"
@@ -1178,7 +1205,7 @@ msgid ""
 "loss of precision by tracking multiple intermediate partial sums."
 msgstr ""
 "回傳可疊代物件（iterable）中所有值的精確浮點數和。透過追蹤過程中多個部分和"
-"（partial sum）以避免精確度損失。"
+"（partial sum）以避免精密度損失。"
 
 #: ../../library/math.rst:558
 msgid ""
@@ -1189,7 +1216,7 @@ msgid ""
 "least significant bit."
 msgstr ""
 "此演算法準確性奠基於保證 IEEE-754 浮點標準及典型奇進偶捨（half-even）模式。於"
-"有些非 Windows 平台建置時，底層 C 函式庫使用延伸精度加法運算，而可能導致對過"
+"有些非 Windows 平台建置時，底層 C 函式庫使用延伸精密度加法運算，而可能導致對過"
 "程中同一部分和重複捨入，並使其最低有效位不如預期。"
 
 #: ../../library/math.rst:564
@@ -1208,6 +1235,7 @@ msgid ""
 "the length of the vector from the origin to the point given by the "
 "coordinates."
 msgstr ""
+"回傳歐幾里得範數 ``sqrt(sum(x**2 for x in coordinates))``。這是從原點到座標所給定的點之間的向量長度。"
 
 #: ../../library/math.rst:575
 msgid ""
@@ -1215,12 +1243,14 @@ msgid ""
 "hypotenuse of a right triangle using the Pythagorean theorem, ``sqrt(x*x + "
 "y*y)``."
 msgstr ""
+"對於二維點 ``(x, y)``，這等同於使用畢氏定理計算直角三角形的斜邊，即 "
+"``sqrt(x*x + y*y)``。"
 
 #: ../../library/math.rst:579
 msgid ""
 "Added support for n-dimensional points. Formerly, only the two dimensional "
 "case was supported."
-msgstr ""
+msgstr "新增對 n 維點的支援。先前僅支援二維情況。"
 
 #: ../../library/math.rst:583
 msgid ""
@@ -1228,12 +1258,15 @@ msgid ""
 "(unit in the last place).  More typically, the result is almost always "
 "correctly rounded to within 1/2 ulp."
 msgstr ""
+"改進了演算法的精確度，使最大誤差低於 1 ulp（最後一位上的單位值）。更典型的情況是，"
+"結果幾乎總是能正確捨入到 1/2 ulp 以內。"
 
 #: ../../library/math.rst:591
 msgid ""
 "Calculate the product of all the elements in the input *iterable*. The "
 "default *start* value for the product is ``1``."
 msgstr ""
+"計算輸入 *iterable* 中所有元素的乘積。乘積的預設 *start* 起始值為 ``1``。"
 
 #: ../../library/math.rst:594
 msgid ""
@@ -1241,6 +1274,7 @@ msgid ""
 "intended specifically for use with numeric values and may reject non-numeric "
 "types."
 msgstr ""
+"當可疊代物件為空時，回傳起始值。此函式專門設計用於數值運算，可能會拒絕非數值型別。"
 
 #: ../../library/math.rst:603
 msgid "Return the sum of products of values from two iterables *p* and *q*."
@@ -1259,42 +1293,42 @@ msgid ""
 "For float and mixed int/float inputs, the intermediate products and sums are "
 "computed with extended precision."
 msgstr ""
-"對浮點數或混合整數及浮點數的傳入物件，其過程中的乘積及總和皆使用延伸精度計"
+"對浮點數或混合整數及浮點數的傳入物件，其過程中的乘積及總和皆使用延伸精密度計"
 "算。"
 
 #: ../../library/math.rst:618
 msgid "Angular conversion"
-msgstr ""
+msgstr "角度轉換"
 
 #: ../../library/math.rst:622
 msgid "Convert angle *x* from radians to degrees."
-msgstr ""
+msgstr "將角度 *x* 從弧度轉換為度。"
 
 #: ../../library/math.rst:627
 msgid "Convert angle *x* from degrees to radians."
-msgstr ""
+msgstr "將角度 *x* 從度轉換為弧度。"
 
 #: ../../library/math.rst:631
 msgid "Trigonometric functions"
-msgstr ""
+msgstr "三角函式"
 
 #: ../../library/math.rst:635
 msgid ""
 "Return the arc cosine of *x*, in radians. The result is between ``0`` and "
 "``pi``."
-msgstr ""
+msgstr "回傳 *x* 的反餘弦值，以弧度表示。結果介於 ``0`` 與 ``pi`` 之間。"
 
 #: ../../library/math.rst:641
 msgid ""
 "Return the arc sine of *x*, in radians. The result is between ``-pi/2`` and "
 "``pi/2``."
-msgstr ""
+msgstr "回傳 *x* 的反正弦值，以弧度表示。結果介於 ``-pi/2`` 與 ``pi/2`` 之間。"
 
 #: ../../library/math.rst:647
 msgid ""
 "Return the arc tangent of *x*, in radians. The result is between ``-pi/2`` "
 "and ``pi/2``."
-msgstr ""
+msgstr "回傳 *x* 的反正切值，以弧度表示。結果介於 ``-pi/2`` 與 ``pi/2`` 之間。"
 
 #: ../../library/math.rst:653
 msgid ""
@@ -1305,22 +1339,26 @@ msgid ""
 "for the angle. For example, ``atan(1)`` and ``atan2(1, 1)`` are both ``pi/"
 "4``, but ``atan2(-1, -1)`` is ``-3*pi/4``."
 msgstr ""
+"回傳 ``atan(y / x)``，以弧度表示。結果介於 ``-pi`` 與 ``pi`` 之間。從原點到點 "
+"``(x, y)`` 的平面向量與正 X 軸形成此角度。:func:`atan2` 的重點在於它知道兩個輸入的"
+"正負號，因此能計算出角度所在的正確象限。例如，``atan(1)`` 和 ``atan2(1, 1)`` 都是 "
+"``pi/4``，但 ``atan2(-1, -1)`` 是 ``-3*pi/4``。"
 
 #: ../../library/math.rst:663
 msgid "Return the cosine of *x* radians."
-msgstr "回傳 *x* 弧度的餘弦。"
+msgstr "回傳 *x* 弧度的餘弦值。"
 
 #: ../../library/math.rst:668
 msgid "Return the sine of *x* radians."
-msgstr "回傳 *x* 弧度的正弦。"
+msgstr "回傳 *x* 弧度的正弦值。"
 
 #: ../../library/math.rst:673
 msgid "Return the tangent of *x* radians."
-msgstr "回傳 *x* 弧度的正切。"
+msgstr "回傳 *x* 弧度的正切值。"
 
 #: ../../library/math.rst:677
 msgid "Hyperbolic functions"
-msgstr ""
+msgstr "雙曲函式"
 
 #: ../../library/math.rst:679
 msgid ""
@@ -1328,30 +1366,31 @@ msgid ""
 "are analogs of trigonometric functions that are based on hyperbolas instead "
 "of circles."
 msgstr ""
+"`雙曲函式 <https://en.wikipedia.org/wiki/Hyperbolic_functions>`_\\ 是三角函式的類似物，但基於雙曲線而非圓。"
 
 #: ../../library/math.rst:685
 msgid "Return the inverse hyperbolic cosine of *x*."
-msgstr "回傳 *x* 的反雙曲餘弦。"
+msgstr "回傳 *x* 的反雙曲餘弦值。"
 
 #: ../../library/math.rst:690
 msgid "Return the inverse hyperbolic sine of *x*."
-msgstr "回傳 *x* 的反雙曲正弦。"
+msgstr "回傳 *x* 的反雙曲正弦值。"
 
 #: ../../library/math.rst:695
 msgid "Return the inverse hyperbolic tangent of *x*."
-msgstr "回傳 *x* 的反雙曲正切。"
+msgstr "回傳 *x* 的反雙曲正切值。"
 
 #: ../../library/math.rst:700
 msgid "Return the hyperbolic cosine of *x*."
-msgstr "回傳 *x* 的雙曲餘弦。"
+msgstr "回傳 *x* 的雙曲餘弦值。"
 
 #: ../../library/math.rst:705
 msgid "Return the hyperbolic sine of *x*."
-msgstr "回傳 *x* 的雙曲正弦。"
+msgstr "回傳 *x* 的雙曲正弦值。"
 
 #: ../../library/math.rst:710
 msgid "Return the hyperbolic tangent of *x*."
-msgstr "回傳 *x* 的雙曲正切。"
+msgstr "回傳 *x* 的雙曲正切值。"
 
 #: ../../library/math.rst:714
 msgid "Special functions"
@@ -1362,6 +1401,7 @@ msgid ""
 "Return the `error function <https://en.wikipedia.org/wiki/Error_function>`_ "
 "at *x*."
 msgstr ""
+"回傳在 *x* 處的\\ `誤差函式 <https://en.wikipedia.org/wiki/Error_function>`_\\ 值。"
 
 #: ../../library/math.rst:721
 msgid ""
@@ -1369,6 +1409,8 @@ msgid ""
 "functions such as the `cumulative standard normal distribution <https://"
 "en.wikipedia.org/wiki/Cumulative_distribution_function>`_::"
 msgstr ""
+":func:`erf` 函式可用於計算傳統的統計函式，例如\\ `累積標準常態分布 <https://"
+"en.wikipedia.org/wiki/Cumulative_distribution_function>`_： ::"
 
 #: ../../library/math.rst:725
 msgid ""
@@ -1376,6 +1418,9 @@ msgid ""
 "    'Cumulative distribution function for the standard normal distribution'\n"
 "    return (1.0 + erf(x / sqrt(2.0))) / 2.0"
 msgstr ""
+"def phi(x):\n"
+"    '標準常態分布的累積分布函式'\n"
+"    return (1.0 + erf(x / sqrt(2.0))) / 2.0"
 
 #: ../../library/math.rst:734
 msgid ""
@@ -1385,18 +1430,23 @@ msgid ""
 "from one would cause a `loss of significance <https://en.wikipedia.org/wiki/"
 "Loss_of_significance>`_\\."
 msgstr ""
+"回傳在 *x* 處的互補誤差函式值。`互補誤差函式 <https://en.wikipedia.org/wiki/"
+"Error_function>`_\\ 定義為 ``1.0 - erf(x)``。此函式用於較大的 *x* 值，因為在該情況下"
+"從一減去會導致\\ `顯著性損失 <https://en.wikipedia.org/wiki/"
+"Loss_of_significance>`_。"
 
 #: ../../library/math.rst:745
 msgid ""
 "Return the `Gamma function <https://en.wikipedia.org/wiki/Gamma_function>`_ "
 "at *x*."
 msgstr ""
+"回傳在 *x* 處的 `Gamma 函式 <https://en.wikipedia.org/wiki/Gamma_function>`_\\ 值。"
 
 #: ../../library/math.rst:753
 msgid ""
 "Return the natural logarithm of the absolute value of the Gamma function at "
 "*x*."
-msgstr ""
+msgstr "回傳在 *x* 處 Gamma 函式絕對值的自然對數。"
 
 #: ../../library/math.rst:760
 msgid "Constants"
@@ -1404,11 +1454,11 @@ msgstr "常數"
 
 #: ../../library/math.rst:764
 msgid "The mathematical constant *π* = 3.141592..., to available precision."
-msgstr ""
+msgstr "數學常數 *π* = 3.141592...，精確至可用精密度。"
 
 #: ../../library/math.rst:769
 msgid "The mathematical constant *e* = 2.718281..., to available precision."
-msgstr ""
+msgstr "數學常數 *e* = 2.718281...，精確至可用精密度。"
 
 #: ../../library/math.rst:774
 msgid ""
@@ -1418,12 +1468,17 @@ msgid ""
 "(still) Wrong <https://vimeo.com/147792667>`_, and start celebrating `Tau "
 "day <https://tauday.com/>`_ by eating twice as much pie!"
 msgstr ""
+"數學常數 *τ* = 6.283185...，精確至可用精密度。Tau 是一個圓常數，等於 2\\ *π*，"
+"即圓的周長與半徑的比值。若想了解更多關於 Tau 的資訊，請觀看 Vi Hart 的影片 "
+"`Pi is (still) Wrong <https://vimeo.com/147792667>`_，並開始慶祝 `Tau 日 "
+"<https://tauday.com/>`_，吃兩倍的派吧！"
 
 #: ../../library/math.rst:785
 msgid ""
 "A floating-point positive infinity.  (For negative infinity, use ``-"
 "math.inf``.)  Equivalent to the output of ``float('inf')``."
 msgstr ""
+"浮點數正無限值。（對於負無限值，請使用 ``-math.inf``。）等同於 ``float('inf')`` 的輸出。"
 
 #: ../../library/math.rst:793
 msgid ""
@@ -1434,10 +1489,14 @@ msgid ""
 "check whether a number is a NaN, use the :func:`isnan` function to test for "
 "NaNs instead of ``is`` or ``==``. Example:"
 msgstr ""
+"浮點數「非數值」（NaN）值。等同於 ``float('nan')`` 的輸出。根據 `IEEE-754 標準 "
+"<https://en.wikipedia.org/wiki/IEEE_754>`_\\ 的要求，``math.nan`` 和 "
+"``float('nan')`` 不被認為等於任何其他數值，包括它們自身。若要檢查一個數是否為 "
+"NaN，請使用 :func:`isnan` 函式而非 ``is`` 或 ``==``。範例："
 
 #: ../../library/math.rst:813
 msgid "It is now always available."
-msgstr ""
+msgstr "現在總是可用。"
 
 #: ../../library/math.rst:819
 msgid ""
@@ -1453,6 +1512,13 @@ msgid ""
 "there are some exceptions to this rule, for example ``pow(float('nan'), "
 "0.0)`` or ``hypot(float('nan'), float('inf'))``."
 msgstr ""
+":mod:`math` 模組大部分由平臺 C 數學函式庫的輕量包裝函式組成。例外情況下的行為在適當"
+"時遵循 C99 標準的附錄 F。目前的實作會對無效操作（如 ``sqrt(-1.0)`` 或 "
+"``log(0.0)``，C99 附錄 F 建議發出無效操作或除以零的訊號）引發 :exc:`ValueError`，並"
+"對溢位結果（例如 ``exp(1000.0)``）引發 :exc:`OverflowError`。除非一個或多個輸入引數"
+"是 NaN，否則上述函式不會回傳 NaN；在該情況下，大多數函式會回傳 NaN，但（同樣遵循 "
+"C99 附錄 F）此規則有一些例外，例如 ``pow(float('nan'), 0.0)`` 或 "
+"``hypot(float('nan'), float('inf'))``。"
 
 #: ../../library/math.rst:831
 msgid ""
@@ -1460,6 +1526,8 @@ msgid ""
 "NaNs, and behavior for signaling NaNs remains unspecified. Typical behavior "
 "is to treat all NaNs as though they were quiet."
 msgstr ""
+"請注意，Python 不會區分訊號型 NaN（signaling NaN）與安靜型 NaN（quiet NaN），且訊號型 "
+"NaN 的行為仍未指定。典型的行為是將所有 NaN 視為安靜型 NaN。"
 
 #: ../../library/math.rst:838
 msgid "Module :mod:`cmath`"
@@ -1467,4 +1535,4 @@ msgstr ":mod:`cmath` 模組"
 
 #: ../../library/math.rst:839
 msgid "Complex number versions of many of these functions."
-msgstr ""
+msgstr "這些函式的複數版本。"