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Arrow (symbol)

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This article is about the symbol. For other uses, see Arrow (disambiguation).
"⇈", "⇅", and "⇶" redirect here. For the mathematical notation for tetration, see Knuth's up-arrow notation. For the quantum theory of electron spin, see Spin (physics). For the political symbol of the Iron Front, see Three Arrows.
This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.
Advertising billboards in Okazaki, Japan, featuring many different arrow symbols

An arrow is a graphical symbol, such as ← or →, or a pictogram, used to point or indicate direction. In its simplest form, an arrow is a triangle, chevron, or concave kite, usually affixed to a line segment or rectangle,[1] and in more complex forms a representation of an actual arrow (e.g. ➵ U+27B5). The direction indicated by an arrow is the one along the length of the line or rectangle toward the single pointed end.

History

An older (medieval) convention is the manicule (pointing hand, 👈). Pedro Reinel in c. 1504 first used the fleur-de-lis as indicating north in a compass rose; the convention of marking the eastern direction with a cross is older (medieval).[2] Use of the arrow symbol does not appear to pre-date the 18th century. An early arrow symbol is found in an illustration of Bernard Forest de Bélidor's treatise L'architecture hydraulique, printed in France in 1737. The arrow is here used to illustrate the direction of the flow of water and of the water wheel's rotation. At about the same time, arrow symbols were used to indicate the flow of rivers in maps.[3]

A trend toward abstraction, in which the arrow's fletching is removed, can be observed in the mid-to-late 19th century. The arrow can be seen in the work of Paul Klee. In a further abstraction of the symbol, John Richard Green's A Short History of the English People of 1874 contained maps by cartographer Emil Reich, which indicated army movements by curved lines, with solid triangular arrowheads placed intermittently along the lines.[4]

Use of arrow symbols in mathematical notation is still younger and developed in the first half of the 20th century.[5] David Hilbert in 1922 introduced the arrow symbol representing logical implication. The double-headed arrow representing logical equivalence was introduced by Albrecht Becker in Die Aristotelische Theorie der Möglichkeitsschlüsse, Berlin, 1933.[4]

Usage

An exit sign with an arrow to indicate the exit is to the left

Arrows are universally recognised for indicating directions.[1] They are widely used on signage and for wayfinding,[1] and are often used in road surface markings.

Upward arrows are often used to indicate an increase in a numerical value, and downward arrows indicate a decrease.

In mathematical logic, a right-facing arrow indicates material conditional, and a left-right (bidirectional) arrow indicates if and only if, an upwards arrow indicates the NAND operator (negation of conjunction), an downwards arrow indicates the NOR operator (negation of disjunction).

Unicode

In Unicode, the block Arrows occupies the hexadecimal range U+2190–U+21FF, as described below.

Symbol Name Symbol Name Symbol Name Symbol Name
Hex Hex Hex Hex
Picture of this symbol Picture of this symbol Picture of this symbol Picture of this symbol
← Leftwards Arrow ↬ Rightwards Arrow With Loop ⇈ Upwards Paired Arrows ⇤ Leftwards Arrow To Bar
U+2190 U+21AC U+21C8 U+21E4
↑ Upwards Arrow ↭ Left Right Wave Arrow ⇉ Rightwards Paired Arrows ⇥ Rightwards Arrow To Bar
U+2191 U+21AD U+21C9 U+21E5
→ Rightwards Arrow ↮ Left Right Arrow With Stroke ⇊ Downwards Paired Arrows ⇦ Leftwards Thick Arrow
U+2192 U+21AE U+21CA U+21E6
↓ Downwards Arrow ↯ Downwards Zigzag Arrow ⇋ Leftwards Harpoon Over Rightwards Harpoon ⇧ Upwards Thick Arrow
U+2193 U+21AF U+21CB U+21E7
↔ Left Right Arrow ↰ Upwards Arrow With Tip Leftwards ⇌ Rightwards Harpoon Over Leftwards Harpoon ⇨ Rightwards Thick Arrow
U+2194 U+21B0 U+21CC U+21E8
↕ Up Down Arrow ↱ Upwards Arrow With Tip Rightwards ⇍ Leftwards Double Arrow With Stroke ⇩ Downwards Thick Arrow
U+2195 U+21B1 U+21CD U+21E9
↖ North West Arrow ↲ Downwards Arrow With Tip Leftwards ⇎ Left Right Double Arrow With Stroke ⇪ Upwards Thick Arrow From Bar
U+2196 U+21B2 U+21CE U+21EA
↗ North East Arrow ↳ Downwards Arrow With Tip Rightwards ⇏ Rightwards Double Arrow With Stroke ⇫ Upwards Thick Arrow On Pedestal
U+2197 U+21B3 U+21CF U+21EB
↘ South East Arrow ↴ Rightwards Arrow With Corner Downwards ⇐ Leftwards Double Arrow ⇬ Upwards Thick Arrow On Pedestal With Horizontal Bar
U+2198 U+21B4 U+21D0 U+21EC
↙ South West Arrow ↵ Downwards Arrow With Corner Leftwards ⇑ Upwards Double Arrow ⇭ Upwards Thick Arrow On Pedestal With Vertical Bar
U+2199 U+21B5 U+21D1 U+21ED
↚ Leftwards Arrow With Stroke ↶ Anticlockwise Top Semicircle Arrow ⇒ Rightwards Double Arrow ⇮ Upwards Thick Double Arrow
U+219A U+21B6 U+21D2 U+21EE
↛ Rightwards Arrow With Stroke ↷ Clockwise Top Semicircle Arrow ⇓ Downwards Double Arrow ⇯ Upwards Thick Double Arrow On Pedestal
U+219B U+21B7 U+21D3 U+21EF
↜ Leftwards Wave Arrow ↸ North West Arrow To Long Bar ⇔ Left Right Double Arrow ⇰ Rightwards Thick Arrow From Wall
U+219C U+21B8 U+21D4 U+21F0
↝ Rightwards Wave Arrow ↹ Leftwards Arrow To Bar Over Rightwards Arrow To Bar ⇕ Up Down Double Arrow ⇱ North West Arrow To Corner
U+219D U+21B9 U+21D5 U+21F1
↞ Leftwards Two Headed Arrow ↺ Anticlockwise Open Circle Arrow ⇖ North West Double Arrow ⇲ South East Arrow To Corner
U+219E U+21BA U+21D6 U+21F2
↟ Upwards Two Headed Arrow ↻ Clockwise Open Circle Arrow ⇗ North East Double Arrow ⇳ Up Down Thick Arrow
U+219F U+21BB U+21D7 U+21F3
↠ Rightwards Two Headed Arrow ↼ Leftwards Harpoon With Barb Upwards ⇘ South East Double Arrow ⇴ Right Arrow With Small Circle
U+21A0 U+21BC U+21D8 U+21F4
↡ Downwards Two Headed Arrow ↽ Leftwards Harpoon With Barb Downwards ⇙ South West Double Arrow ⇵ Downwards Arrow Leftwards Of Upwards Arrow
U+21A1 U+21BD U+21D9 U+21F5
↢ Leftwards Arrow With Tail ↾ Upwards Harpoon With Barb Rightwards ⇚ Leftwards Triple Arrow ⇶ Three Rightwards Arrows
U+21A2 U+21BE U+21DA U+21F6
↣ Rightwards Arrow With Tail ↿ Upwards Harpoon With Barb Leftwards ⇛ Rightwards Triple Arrow ⇷ Leftwards Arrow With Vertical Stroke
U+21A3 U+21BF U+21DB U+21F7
↤ Leftwards Arrow From Bar ⇀ Rightwards Harpoon With Barb Upwards ⇜ Leftwards Squiggle Arrow ⇸ Rightwards Arrow With Vertical Stroke
U+21A4 U+21C0 U+21DC U+21F8
↥ Upwards Arrow From Bar ⇁ Rightwards Harpoon With Barb Downwards ⇝ Rightwards Squiggle Arrow ⇹ Left Right Arrow With Vertical Stroke
U+21A5 U+21C1 U+21DD U+21F9
↦ Rightwards Arrow From Bar ⇂ Downwards Harpoon With Barb Rightwards ⇞ Upwards Arrow With Double Stroke ⇺ Leftwards Arrow With Double Vertical Stroke
U+21A6 U+21C2 U+21DE U+21FA
↧ Downwards Arrow From Bar ⇃ Downwards Harpoon With Barb Leftwards ⇟ Downwards Arrow With Double Stroke ⇻ Rightwards Arrow With Double Vertical Stroke
U+21A7 U+21C3 U+21DF U+21FB
↨ Up Down Arrow With Base ⇄ Rightwards Arrow Over Leftwards Arrow ⇠ Leftwards Dashed Arrow ⇼ Left Right Arrow With Double Vertical Stroke
U+21A8 U+21C4 U+21E0 U+21FC
↩ Leftwards Arrow With Hook ⇅ Upwards Arrow Leftwards Of Downwards Arrow ⇡ Upwards Dashed Arrow ⇽ Leftwards Open-Headed Arrow
U+21A9 U+21C5 U+21E1 U+21FD
↪ Rightwards Arrow With Hook ⇆ Leftwards Arrow Over Rightwards Arrow ⇢ Rightwards Dashed Arrow ⇾ Rightwards Open-Headed Arrow
U+21AA U+21C6 U+21E2 U+21FE
↫ Leftwards Arrow With Loop ⇇ Leftwards Paired Arrows ⇣ Downwards Dashed Arrow ⇿ Left Right Open-Headed Arrow
U+21AB U+21C7 U+21E3 U+21FF

By block

Arrows[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+219x ← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↜ ↝ ↞ ↟
U+21Ax ↠ ↡ ↢ ↣ ↤ ↥ ↦ ↧ ↨ ↩ ↪ ↫ ↬ ↭ ↮ ↯
U+21Bx ↰ ↱ ↲ ↳ ↴ ↵ ↶ ↷ ↸ ↹ ↺ ↻ ↼ ↽ ↾ ↿
U+21Cx ⇀ ⇁ ⇂ ⇃ ⇄ ⇅ ⇆ ⇇ ⇈ ⇉ ⇊ ⇋ ⇌ ⇍ ⇎ ⇏
U+21Dx ⇐ ⇑ ⇒ ⇓ ⇔ ⇕ ⇖ ⇗ ⇘ ⇙ ⇚ ⇛ ⇜ ⇝ ⇞ ⇟
U+21Ex ⇠ ⇡ ⇢ ⇣ ⇤ ⇥ ⇦ ⇧ ⇨ ⇩ ⇪ ⇫ ⇬ ⇭ ⇮ ⇯
U+21Fx ⇰ ⇱ ⇲ ⇳ ⇴ ⇵ ⇶ ⇷ ⇸ ⇹ ⇺ ⇻ ⇼ ⇽ ⇾ ⇿
Notes
1.^ As of Unicode version 16.0
Dingbats[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+270x ✀ ✁ ✂ ✃ ✄ ✅ ✆ ✇ ✈ ✉ ✊ ✋ ✌ ✍ ✎ ✏
U+271x ✐ ✑ ✒ ✓ ✔ ✕ ✖ ✗ ✘ ✙ ✚ ✛ ✜ ✝ ✞ ✟
U+272x ✠ ✡ ✢ ✣ ✤ ✥ ✦ ✧ ✨ ✩ ✪ ✫ ✬ ✭ ✮ ✯
U+273x ✰ ✱ ✲ ✳ ✴ ✵ ✶ ✷ ✸ ✹ ✺ ✻ ✼ ✽ ✾ ✿
U+274x ❀ ❁ ❂ ❃ ❄ ❅ ❆ ❇ ❈ ❉ ❊ ❋ ❌ ❍ ❎ ❏
U+275x ❐ ❑ ❒ ❓ ❔ ❕ ❖ ❗ ❘ ❙ ❚ ❛ ❜ ❝ ❞ ❟
U+276x ❠ ❡ ❢ ❣ ❤ ❥ ❦ ❧ ❨ ❩ ❪ ❫ ❬ ❭ ❮ ❯
U+277x ❰ ❱ ❲ ❳ ❴ ❵ ❶ ❷ ❸ ❹ ❺ ❻ ❼ ❽ ❾ ❿
U+278x ➀ ➁ ➂ ➃ ➄ ➅ ➆ ➇ ➈ ➉ ➊ ➋ ➌ ➍ ➎ ➏
U+279x ➐ ➑ ➒ ➓ ➔ ➕ ➖ ➗ ➘ ➙ ➚ ➛ ➜ ➝ ➞ ➟
U+27Ax ➠ ➡ ➢ ➣ ➤ ➥ ➦ ➧ ➨ ➩ ➪ ➫ ➬ ➭ ➮ ➯
U+27Bx ➰ ➱ ➲ ➳ ➴ ➵ ➶ ➷ ➸ ➹ ➺ ➻ ➼ ➽ ➾ ➿
Notes
1.^ As of Unicode version 16.0
Miscellaneous Symbols and Arrows[1][2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+2B0x ⬀ ⬁ ⬂ ⬃ ⬄ ⬅ ⬆ ⬇ ⬈ ⬉ ⬊ ⬋ ⬌ ⬍ ⬎ ⬏
U+2B1x ⬐ ⬑ ⬒ ⬓ ⬔ ⬕ ⬖ ⬗ ⬘ ⬙ ⬚ ⬛ ⬜ ⬝ ⬞ ⬟
U+2B2x ⬠ ⬡ ⬢ ⬣ ⬤ ⬥ ⬦ ⬧ ⬨ ⬩ ⬪ ⬫ ⬬ ⬭ ⬮ ⬯
U+2B3x ⬰ ⬱ ⬲ ⬳ ⬴ ⬵ ⬶ ⬷ ⬸ ⬹ ⬺ ⬻ ⬼ ⬽ ⬾ ⬿
U+2B4x ⭀ ⭁ ⭂ ⭃ ⭄ ⭅ ⭆ ⭇ ⭈ ⭉ ⭊ ⭋ ⭌ ⭍ ⭎ ⭏
U+2B5x ⭐ ⭑ ⭒ ⭓ ⭔ ⭕ ⭖ ⭗ ⭘ ⭙ ⭚ ⭛ ⭜ ⭝ ⭞ ⭟
U+2B6x ⭠ ⭡ ⭢ ⭣ ⭤ ⭥ ⭦ ⭧ ⭨ ⭩ ⭪ ⭫ ⭬ ⭭ ⭮ ⭯
U+2B7x ⭰ ⭱ ⭲ ⭳ ⭶ ⭷ ⭸ ⭹ ⭺ ⭻ ⭼ ⭽ ⭾ ⭿
U+2B8x ⮀ ⮁ ⮂ ⮃ ⮄ ⮅ ⮆ ⮇ ⮈ ⮉ ⮊ ⮋ ⮌ ⮍ ⮎ ⮏
U+2B9x ⮐ ⮑ ⮒ ⮓ ⮔ ⮕ ⮗ ⮘ ⮙ ⮚ ⮛ ⮜ ⮝ ⮞ ⮟
U+2BAx ⮠ ⮡ ⮢ ⮣ ⮤ ⮥ ⮦ ⮧ ⮨ ⮩ ⮪ ⮫ ⮬ ⮭ ⮮ ⮯
U+2BBx ⮰ ⮱ ⮲ ⮳ ⮴ ⮵ ⮶ ⮷ ⮸ ⮹ ⮺ ⮻ ⮼ ⮽ ⮾ ⮿
U+2BCx ⯀ ⯁ ⯂ ⯃ ⯄ ⯅ ⯆ ⯇ ⯈ ⯉ ⯊ ⯋ ⯌ ⯍ ⯎ ⯏
U+2BDx ⯐ ⯑ ⯒ ⯓ ⯔ ⯕ ⯖ ⯗ ⯘ ⯙ ⯚ ⯛ ⯜ ⯝ ⯞ ⯟
U+2BEx ⯠ ⯡ ⯢ ⯣ ⯤ ⯥ ⯦ ⯧ ⯨ ⯩ ⯪ ⯫ ⯬ ⯭ ⯮ ⯯
U+2BFx ⯰ ⯱ ⯲ ⯳ ⯴ ⯵ ⯶ ⯷ ⯸ ⯹ ⯺ ⯻ ⯼ ⯽ ⯾ ⯿
Notes
1.^ As of Unicode version 16.0
2.^ Grey areas indicate non-assigned code points
Supplemental Arrows-A[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+27Fx ⟰ ⟱ ⟲ ⟳ ⟴ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟻ ⟼ ⟽ ⟾ ⟿
Notes
1.^ As of Unicode version 16.0
Supplemental Arrows-B[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+290x ⤀ ⤁ ⤂ ⤃ ⤄ ⤅ ⤆ ⤇ ⤈ ⤉ ⤊ ⤋ ⤌ ⤍ ⤎ ⤏
U+291x ⤐ ⤑ ⤒ ⤓ ⤔ ⤕ ⤖ ⤗ ⤘ ⤙ ⤚ ⤛ ⤜ ⤝ ⤞ ⤟
U+292x ⤠ ⤡ ⤢ ⤣ ⤤ ⤥ ⤦ ⤧ ⤨ ⤩ ⤪ ⤫ ⤬ ⤭ ⤮ ⤯
U+293x ⤰ ⤱ ⤲ ⤳ ⤴ ⤵ ⤶ ⤷ ⤸ ⤹ ⤺ ⤻ ⤼ ⤽ ⤾ ⤿
U+294x ⥀ ⥁ ⥂ ⥃ ⥄ ⥅ ⥆ ⥇ ⥈ ⥉ ⥊ ⥋ ⥌ ⥍ ⥎ ⥏
U+295x ⥐ ⥑ ⥒ ⥓ ⥔ ⥕ ⥖ ⥗ ⥘ ⥙ ⥚ ⥛ ⥜ ⥝ ⥞ ⥟
U+296x ⥠ ⥡ ⥢ ⥣ ⥤ ⥥ ⥦ ⥧ ⥨ ⥩ ⥪ ⥫ ⥬ ⥭ ⥮ ⥯
U+297x ⥰ ⥱ ⥲ ⥳ ⥴ ⥵ ⥶ ⥷ ⥸ ⥹ ⥺ ⥻ ⥼ ⥽ ⥾ ⥿
Notes
1.^ As of Unicode version 16.0
Supplemental Arrows-C[1][2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+1F80x 🠀 🠁 🠂 🠃 🠄 🠅 🠆 🠇 🠈 🠉 🠊 🠋
U+1F81x 🠐 🠑 🠒 🠓 🠔 🠕 🠖 🠗 🠘 🠙 🠚 🠛 🠜 🠝 🠞 🠟
U+1F82x 🠠 🠡 🠢 🠣 🠤 🠥 🠦 🠧 🠨 🠩 🠪 🠫 🠬 🠭 🠮 🠯
U+1F83x 🠰 🠱 🠲 🠳 🠴 🠵 🠶 🠷 🠸 🠹 🠺 🠻 🠼 🠽 🠾 🠿
U+1F84x 🡀 🡁 🡂 🡃 🡄 🡅 🡆 🡇
U+1F85x 🡐 🡑 🡒 🡓 🡔 🡕 🡖 🡗 🡘 🡙
U+1F86x 🡠 🡡 🡢 🡣 🡤 🡥 🡦 🡧 🡨 🡩 🡪 🡫 🡬 🡭 🡮 🡯
U+1F87x 🡰 🡱 🡲 🡳 🡴 🡵 🡶 🡷 🡸 🡹 🡺 🡻 🡼 🡽 🡾 🡿
U+1F88x 🢀 🢁 🢂 🢃 🢄 🢅 🢆 🢇
U+1F89x 🢐 🢑 🢒 🢓 🢔 🢕 🢖 🢗 🢘 🢙 🢚 🢛 🢜 🢝 🢞 🢟
U+1F8Ax 🢠 🢡 🢢 🢣 🢤 🢥 🢦 🢧 🢨 🢩 🢪 🢫 🢬 🢭
U+1F8Bx 🢰 🢱 🢲 🢳 🢴 🢵 🢶 🢷 🢸 🢹 🢺 🢻
U+1F8Cx 🣀 🣁
U+1F8Dx
U+1F8Ex
U+1F8Fx
Notes
1.^ As of Unicode version 16.0
2.^ Grey areas indicate non-assigned code points
Symbols for Legacy Computing[1][2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+1FB0x 🬀 🬁 🬂 🬃 🬄 🬅 🬆 🬇 🬈 🬉 🬊 🬋 🬌 🬍 🬎 🬏
U+1FB1x 🬐 🬑 🬒 🬓 🬔 🬕 🬖 🬗 🬘 🬙 🬚 🬛 🬜 🬝 🬞 🬟
U+1FB2x 🬠 🬡 🬢 🬣 🬤 🬥 🬦 🬧 🬨 🬩 🬪 🬫 🬬 🬭 🬮 🬯
U+1FB3x 🬰 🬱 🬲 🬳 🬴 🬵 🬶 🬷 🬸 🬹 🬺 🬻 🬼 🬽 🬾 🬿
U+1FB4x 🭀 🭁 🭂 🭃 🭄 🭅 🭆 🭇 🭈 🭉 🭊 🭋 🭌 🭍 🭎 🭏
U+1FB5x 🭐 🭑 🭒 🭓 🭔 🭕 🭖 🭗 🭘 🭙 🭚 🭛 🭜 🭝 🭞 🭟
U+1FB6x 🭠 🭡 🭢 🭣 🭤 🭥 🭦 🭧 🭨 🭩 🭪 🭫 🭬 🭭 🭮 🭯
U+1FB7x 🭰 🭱 🭲 🭳 🭴 🭵 🭶 🭷 🭸 🭹 🭺 🭻 🭼 🭽 🭾 🭿
U+1FB8x 🮀 🮁 🮂 🮃 🮄 🮅 🮆 🮇 🮈 🮉 🮊 🮋 🮌 🮍 🮎 🮏
U+1FB9x 🮐 🮑 🮒 🮔 🮕 🮖 🮗 🮘 🮙 🮚 🮛 🮜 🮝 🮞 🮟
U+1FBAx 🮠 🮡 🮢 🮣 🮤 🮥 🮦 🮧 🮨 🮩 🮪 🮫 🮬 🮭 🮮 🮯
U+1FBBx 🮰 🮱 🮲 🮳 🮴 🮵 🮶 🮷 🮸 🮹 🮺 🮻 🮼 🮽 🮾 🮿
U+1FBCx 🯀 🯁 🯂 🯃 🯄 🯅 🯆 🯇 🯈 🯉 🯊 🯋 🯌 🯍 🯎 🯏
U+1FBDx 🯐 🯑 🯒 🯓 🯔 🯕 🯖 🯗 🯘 🯙 🯚 🯛 🯜 🯝 🯞 🯟
U+1FBEx 🯠 🯡 🯢 🯣 🯤 🯥 🯦 🯧 🯨 🯩 🯪 🯫 🯬 🯭 🯮 🯯
U+1FBFx 🯰 🯱 🯲 🯳 🯴 🯵 🯶 🯷 🯸 🯹
Notes
1.^ As of Unicode version 16.0
2.^ Grey areas indicate non-assigned code points

Additional arrows can be found in the Combining Diacritical Marks, Combining Diacritical Marks Extended, Combining Diacritical Marks for Symbols, Halfwidth and Fullwidth Forms, Miscellaneous Mathematical Symbols-B, Miscellaneous Symbols and Pictographs, Miscellaneous Technical, Modifier Tone Letters and Spacing Modifier Letters Unicode blocks.

See also

References

  1. ^ a b c "How to Design and Use Arrows on Signage for Wayfinding". Travel wayfinding. 7 April 2019. Key Point 5; Key Point 9. Retrieved 17 July 2019.
  2. ^ The American Revolution, 1775-1783: An Atlas of 18th Century Maps and Charts, Theatres of Operations, United States Naval History Division (1972), 14f.
  3. ^ E. H. Dobrich, "Pictorial Instructions" in: H. Barlow et al. (eds.), Images and understanding, Cambridge University Press (1990).
  4. ^ a b History of the Arrow, American Printing History Society (2015).
  5. ^ Green, J.J, Rossberg, M., and Ebert, P.A., : The Convenience of the Typesetter; Notation and Typography in Frege’s Grundgesetze der Arithmetik, Bulletin of Symbolic Logic 21 (2015): 13-30, fn. 17 [1] | DOI
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