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Title: Greek Letters in Mathematics
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Series: Greek Letters in Mathematics
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YouTube-Title: Greek Letters in Mathematics
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Subtitle on GitHub: greek01_sub_eng.srt
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Timestamps
00:00 Introduction
00:30 Alpha
01:00 Beta
01:17 Gamma
01:36 Delta
01:57 Epsilon
02:19 Zeta
02:27 Eta
02:50 Theta
03:10 Iota
03:31 Kappa
03:55 Lambda
04:12 Mu
04:32 Nu
04:53 Xi
05:17 Omicron
05:39 Pi
06:02 Rho
06:15 Sigma
06:40 Tau
07:03 Upsilon
07:32 Phi
08:00 Chi
08:19 Psi
08:37 Omega
09:10 Credits
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Subtitle in English
1 00:00:00,200 –> 00:00:03,300 Hello and welcome to this video about greek
2 00:00:03,300 –> 00:00:05,060 letters we use in mathematics.
3 00:00:06,000 –> 00:00:07,960 But first I want to thank all the
4 00:00:07,960 –> 00:00:09,900 nice people that support this channel on Steady
5 00:00:09,900 –> 00:00:10,760 or Paypal.
6 00:00:11,500 –> 00:00:14,960 Now in natural science and mathematics some greek
7 00:00:14,960 –> 00:00:18,100 letters are often used, because they nicely extend
8 00:00:18,100 –> 00:00:20,380 the symbol set of the latin alphabet.
9 00:00:21,600 –> 00:00:24,220 Indeed the pronunciation of the letters differ a
10 00:00:24,220 –> 00:00:24,500 lot.
11 00:00:24,980 –> 00:00:27,200 Therefore the most important part of this video
12 00:00:27,200 –> 00:00:29,120 is that I can show you how to
13 00:00:29,120 –> 00:00:29,900 write the letters.
14 00:00:30,580 –> 00:00:32,900 So then let’s immediately start with the first
15 00:00:32,900 –> 00:00:35,120 one alpha or alfa.
16 00:00:35,620 –> 00:00:38,360 The lowercase letter is often used and written
17 00:00:38,360 –> 00:00:39,040 like this.
18 00:00:39,800 –> 00:00:42,800 The uppercase letter looks like an A, therefore
19 00:00:42,800 –> 00:00:44,520 we don’t use it as a symbol.
20 00:00:45,800 –> 00:00:48,140 In the case you use LaTeX you generate
21 00:00:48,140 –> 00:00:51,500 the lowercase one by backslash alpha and the
22 00:00:51,500 –> 00:00:53,200 uppercase one simply by A.
23 00:00:53,980 –> 00:00:56,660 And then you see the output looks like
24 00:00:56,660 –> 00:00:57,160 this.
25 00:00:58,030 –> 00:01:00,100 Ok then let’s go to the next one
26 00:01:00,100 –> 00:01:01,300 which is beta.
27 00:01:02,520 –> 00:01:05,040 There we also only use the lowercase one
28 00:01:05,040 –> 00:01:06,380 which looks like this.
29 00:01:07,060 –> 00:01:10,420 Because capital beta again looks like B.
30 00:01:11,560 –> 00:01:15,180 Also here in LaTeX backslash beta gives us
31 00:01:15,180 –> 00:01:16,620 this nice output here.
32 00:01:17,760 –> 00:01:19,940 Ok then the third one is gamma.
33 00:01:20,740 –> 00:01:23,400 Where the lowercase letter looks like this and
34 00:01:23,400 –> 00:01:25,140 the capital one is this.
35 00:01:25,820 –> 00:01:28,400 Now for LaTeX we have two commands.
36 00:01:28,740 –> 00:01:30,740 One with the lowercase g and one with
37 00:01:30,740 –> 00:01:31,460 the capital G.
38 00:01:32,140 –> 00:01:34,480 And as before you see we get this
39 00:01:34,480 –> 00:01:35,440 nice output here.
40 00:01:36,500 –> 00:01:38,660 Then the next on the list is delta.
41 00:01:39,760 –> 00:01:41,500 Indeed this is what you often see in
42 00:01:41,500 –> 00:01:42,000 mathematics.
43 00:01:42,320 –> 00:01:44,420 This is the lowercase one and this is
44 00:01:44,420 –> 00:01:45,280 the capital one.
45 00:01:46,260 –> 00:01:48,460 And now you might already guess the corresponding
46 00:01:48,460 –> 00:01:52,020 LaTeX commands with lowercase d and capital D.
47 00:01:52,700 –> 00:01:55,420 And as before we get a very nice
48 00:01:55,420 –> 00:01:56,100 output here.
49 00:01:57,220 –> 00:02:00,420 Now immediately after delta we find epsilon in
50 00:02:00,420 –> 00:02:00,820 the list.
51 00:02:01,760 –> 00:02:03,720 And there we only use the lowercase one
52 00:02:03,720 –> 00:02:04,780 which looks like this.
53 00:02:05,000 –> 00:02:07,440 Because the capital one is just an E.
54 00:02:08,360 –> 00:02:11,680 Indeed in LaTeX you find two variants for
55 00:02:11,680 –> 00:02:13,480 the lowercase letter you can use.
56 00:02:14,400 –> 00:02:16,580 However as you can see most of the
57 00:02:16,580 –> 00:02:18,980 time we would prefer the second one here.
58 00:02:19,660 –> 00:02:22,460 Ok then next we have zeta.
59 00:02:23,500 –> 00:02:25,680 There we only use the lowercase one which
60 00:02:25,680 –> 00:02:26,740 I draw like this.
61 00:02:27,580 –> 00:02:29,520 And as you might already guess the capital
62 00:02:29,520 –> 00:02:30,800 one is just a Z.
63 00:02:31,420 –> 00:02:34,340 Ok then the command backslash zeta gives us
64 00:02:34,340 –> 00:02:36,100 this very nice symbol here.
65 00:02:37,000 –> 00:02:39,000 The next letter on the list is eta
66 00:02:39,000 –> 00:02:41,580 where the lowercase one looks like this.
67 00:02:42,400 –> 00:02:44,800 And the capital one is just an H.
68 00:02:45,880 –> 00:02:48,120 And as before this is how it works
69 00:02:48,120 –> 00:02:48,840 in LaTeX.
70 00:02:49,680 –> 00:02:52,040 Now the next one I find very interesting
71 00:02:52,040 –> 00:02:53,580 and it’s theta.
72 00:02:54,400 –> 00:02:57,140 The lowercase letter you either do in this
73 00:02:57,140 –> 00:02:58,920 way or in this way.
74 00:02:59,740 –> 00:03:02,020 And the capital one looks like the first
75 00:03:02,020 –> 00:03:03,580 lowercase one but thicker.
76 00:03:04,860 –> 00:03:07,840 And indeed both possibilities for the lowercase letter
77 00:03:07,840 –> 00:03:09,580 you find in LaTeX as well.
78 00:03:10,460 –> 00:03:13,100 Now the next one is not often used
79 00:03:13,100 –> 00:03:14,580 and it’s called iota.
80 00:03:15,240 –> 00:03:18,240 Indeed the lowercase one looks like an i
81 00:03:18,240 –> 00:03:19,640 but without the dot.
82 00:03:20,480 –> 00:03:22,100 And the capital one we don’t use at
83 00:03:22,100 –> 00:03:24,400 all because it’s simply capital I.
84 00:03:25,460 –> 00:03:27,960 Sometimes the letter is used but then you
85 00:03:27,960 –> 00:03:30,380 see it’s hard to distinguish from a normal
86 00:03:30,380 –> 00:03:30,760 i.
87 00:03:31,500 –> 00:03:34,400 The next one is also hard to distinguish
88 00:03:34,400 –> 00:03:37,120 from a latin letter and it’s called kappa.
89 00:03:37,920 –> 00:03:40,600 It almost looks like a lowercase k.
90 00:03:41,720 –> 00:03:44,220 Indeed the capital one is a capital K.
91 00:03:45,140 –> 00:03:46,980 However since you can make it a little
92 00:03:46,980 –> 00:03:49,320 bit more curved than a normal k we
93 00:03:49,320 –> 00:03:50,460 often use it.
94 00:03:51,340 –> 00:03:54,320 But that’s definitely something you should practise in
95 00:03:54,320 –> 00:03:54,680 writing.
96 00:03:55,660 –> 00:03:58,380 Ok now we reached one popular one called
97 00:03:58,380 –> 00:03:58,960 lambda.
98 00:04:00,220 –> 00:04:02,560 There we use the lowercase one as well
99 00:04:02,560 –> 00:04:03,800 as the capital one.
100 00:04:05,140 –> 00:04:07,680 Therefore again we have two commands we use
101 00:04:07,680 –> 00:04:08,380 in LaTeX.
102 00:04:09,100 –> 00:04:12,460 Now we continue to another important letter called
103 00:04:12,460 –> 00:04:12,820 mu.
104 00:04:13,700 –> 00:04:16,519 There we have this nice lowercase version but
105 00:04:16,519 –> 00:04:18,200 the capital one is just M.
106 00:04:19,140 –> 00:04:21,520 Here the command is nice and short just
107 00:04:21,520 –> 00:04:24,200 backslash mu and we get this nice letter
108 00:04:24,200 –> 00:04:24,560 here.
109 00:04:25,580 –> 00:04:28,060 Ok this was the first half of the
110 00:04:28,060 –> 00:04:28,720 greek alphabet.
111 00:04:29,180 –> 00:04:31,500 The next 12 letters will follow now.
112 00:04:32,240 –> 00:04:34,940 The next one corresponds to n and it’s
113 00:04:34,940 –> 00:04:35,740 called nu.
114 00:04:36,420 –> 00:04:38,880 It’s very important and you should not write
115 00:04:38,880 –> 00:04:39,600 it like a v.
116 00:04:40,400 –> 00:04:42,600 Maybe a curved version like this would be
117 00:04:42,600 –> 00:04:43,200 appropriate.
118 00:04:43,980 –> 00:04:46,160 And the capital one we don’t use because
119 00:04:46,160 –> 00:04:47,340 it’s just capital N.
120 00:04:48,120 –> 00:04:50,900 Indeed you often see this nu in physics
121 00:04:50,900 –> 00:04:51,880 for frequencies.
122 00:04:52,920 –> 00:04:54,860 Ok then the next one I call xi
123 00:04:54,860 –> 00:04:57,780 but often it’s also pronounced xi.
124 00:04:58,680 –> 00:05:01,540 The lowercase letter is written like this.
125 00:05:02,400 –> 00:05:04,620 This is something one has to practise at
126 00:05:04,620 –> 00:05:05,040 the beginning.
127 00:05:05,910 –> 00:05:07,600 And the capital letter is a little bit
128 00:05:07,600 –> 00:05:10,880 funny because it looks like three horizontal lines.
129 00:05:11,860 –> 00:05:14,820 Now as before these two commands produce these
130 00:05:14,820 –> 00:05:15,940 two nice letters.
131 00:05:16,720 –> 00:05:18,820 The next letter in the list is one
132 00:05:18,820 –> 00:05:20,880 we don’t use in mathematics at all.
133 00:05:21,680 –> 00:05:24,020 It’s the omicron or omikron.
134 00:05:24,700 –> 00:05:26,820 We don’t use it because it looks like
135 00:05:26,820 –> 00:05:29,180 a lowercase o or a capital O.
136 00:05:30,160 –> 00:05:33,200 Therefore by default the omikron has no special
137 00:05:33,200 –> 00:05:34,220 LaTeX commands.
138 00:05:35,060 –> 00:05:37,400 However now the next letter on the list
139 00:05:37,400 –> 00:05:38,760 is a very famous one.
140 00:05:39,020 –> 00:05:39,620 It’s pi.
141 00:05:40,740 –> 00:05:43,040 And indeed in mathematics we use the lowercase
142 00:05:43,040 –> 00:05:45,580 version as well as the uppercase version.
143 00:05:46,500 –> 00:05:48,200 Most of the time you see the capital
144 00:05:48,200 –> 00:05:49,800 Pi for the product sign.
145 00:05:51,060 –> 00:05:54,600 Now using backslash pi generates these two important
146 00:05:54,600 –> 00:05:55,040 symbols.
147 00:05:56,260 –> 00:05:58,880 Ok then let’s continue to the next letter
148 00:05:58,880 –> 00:06:01,020 which we often use in physics.
149 00:06:01,900 –> 00:06:04,900 It’s called rho and only the lowercase version
150 00:06:04,900 –> 00:06:05,520 is used.
151 00:06:06,060 –> 00:06:08,620 Because the capital letter is just P.
152 00:06:09,660 –> 00:06:12,040 In fact in LaTeX you have two different
153 00:06:12,040 –> 00:06:14,580 commands to generate a lowercase rho.
154 00:06:15,380 –> 00:06:17,480 Now the next letter on the list is
155 00:06:17,480 –> 00:06:18,720 the famous sigma.
156 00:06:19,740 –> 00:06:22,020 For this the lowercase one as well as
157 00:06:22,020 –> 00:06:24,400 the capital one are used very often.
158 00:06:25,600 –> 00:06:28,080 And indeed in mathematics we use the capital
159 00:06:28,080 –> 00:06:29,680 sigma for the sum sign.
160 00:06:30,460 –> 00:06:32,340 However you can also use it as a
161 00:06:32,340 –> 00:06:35,160 letter, as a variable using the backslash sigma
162 00:06:35,160 –> 00:06:35,600 command.
163 00:06:36,800 –> 00:06:39,020 Now after s comes t, so in the
164 00:06:39,020 –> 00:06:40,880 greek alphabet we find tau.
165 00:06:41,640 –> 00:06:44,640 And there only the lowercase version is used.
166 00:06:46,060 –> 00:06:47,620 You see you write it in a different
167 00:06:47,620 –> 00:06:49,840 way than a normal lowercase t.
168 00:06:50,760 –> 00:06:53,120 And in LaTeX you would use backslash tau
169 00:06:53,120 –> 00:06:53,840 to get it.
170 00:06:54,740 –> 00:06:56,780 Ok now the next letter on the list
171 00:06:56,780 –> 00:06:59,120 could be used, but I see it rarely.
172 00:06:59,680 –> 00:07:03,160 And moreover you find a lot of pronunciations
173 00:07:03,160 –> 00:07:04,000 for ypsilon.
174 00:07:05,040 –> 00:07:07,600 For example you also find it as upsilon.
175 00:07:08,660 –> 00:07:11,480 Personally I wouldn’t use the lowercase version, because
176 00:07:11,480 –> 00:07:13,700 for me it looks like a lowercase v.
177 00:07:14,680 –> 00:07:16,980 However if you don’t draw the capital one
178 00:07:16,980 –> 00:07:19,100 as a Y you can use it.
179 00:07:20,120 –> 00:07:22,800 Indeed by default both letters are in LaTeX
180 00:07:22,800 –> 00:07:25,040 and you can see the capital one is
181 00:07:25,040 –> 00:07:25,780 very unique.
182 00:07:26,660 –> 00:07:28,700 Ok let’s close the list with the last
183 00:07:28,700 –> 00:07:31,560 4 letters, which are all used frequently.
184 00:07:32,260 –> 00:07:34,460 Let’s start with the letter phi.
185 00:07:35,360 –> 00:07:37,540 For this you often see the lowercase version
186 00:07:37,540 –> 00:07:39,540 and also the capital one.
187 00:07:40,520 –> 00:07:42,740 However there is also another version for the
188 00:07:42,740 –> 00:07:45,420 lowercase one, which looks similarly to the capital
189 00:07:45,420 –> 00:07:45,760 one.
190 00:07:46,900 –> 00:07:49,020 Therefore here I think it’s very important, that
191 00:07:49,020 –> 00:07:51,780 you can distinguish the corresponding commands if you
192 00:07:51,780 –> 00:07:52,340 use them.
193 00:07:53,150 –> 00:07:55,260 So there should be no danger of confusion
194 00:07:55,260 –> 00:07:57,560 between the lowercase and the capital letter.
195 00:07:58,340 –> 00:08:00,660 Ok then the next letter on the list
196 00:08:00,660 –> 00:08:01,560 is chi.
197 00:08:02,580 –> 00:08:04,540 It’s not hard to draw and we also
198 00:08:04,540 –> 00:08:07,160 only use the lowercase version, because the capital
199 00:08:07,160 –> 00:08:08,860 one looks like a capital X.
200 00:08:09,840 –> 00:08:11,740 And not so surprising we can use the
201 00:08:11,740 –> 00:08:15,080 command backslash chi to produce this x like
202 00:08:15,080 –> 00:08:15,480 symbol.
203 00:08:16,260 –> 00:08:19,300 Ok now the 23rd letter in the alphabet
204 00:08:19,300 –> 00:08:20,920 is the famous psi.
205 00:08:21,600 –> 00:08:24,680 The lowercase and the uppercase look similarly.
206 00:08:25,160 –> 00:08:27,500 Therefore it’s important that you draw them differently.
207 00:08:28,580 –> 00:08:30,720 However of course with LaTeX you don’t have
208 00:08:30,720 –> 00:08:31,559 a problem at all.
209 00:08:31,799 –> 00:08:33,500 You can distinguish them immediately.
210 00:08:34,700 –> 00:08:36,799 Ok and with this we have reached the
211 00:08:36,799 –> 00:08:39,039 last letter in the list, which is omega.
212 00:08:40,039 –> 00:08:42,320 The lowercase version should not look like a
213 00:08:42,320 –> 00:08:45,480 w and the uppercase version is something like
214 00:08:45,480 –> 00:08:45,880 this.
215 00:08:47,100 –> 00:08:49,960 In fact both symbols we use frequently in
216 00:08:49,960 –> 00:08:50,500 mathematics.
217 00:08:51,300 –> 00:08:54,560 Therefore you can immediately generate them with these
218 00:08:54,560 –> 00:08:55,060 commands.
219 00:08:56,000 –> 00:08:58,100 So we’ve reached the end of the list
220 00:08:58,100 –> 00:09:00,380 and now you know all the greek letters
221 00:09:00,380 –> 00:09:03,260 and the corresponding symbols we use in mathematics.
222 00:09:04,420 –> 00:09:06,900 Therefore i hope this was helpful and that
223 00:09:06,900 –> 00:09:08,340 i see you in the next video.
224 00:09:08,700 –> 00:09:09,200 Bye!
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Last update: 2026-08
