How to make railway timetables (with graphs) - Numberphile

Numberphile November 21, 2021
Video Thumbnail
Numberphile Logo

Numberphile

@numberphile

About

Videos about numbers and mathematics. Videos by Brady Haran since 2011. Our thanks to Jane Street and our Patreon supporters.

Video Description

Featuring Hannah Fry discussing Train Graphs. More links & stuff in full description below ↓↓↓ Hannah's website, including links to her many and varied projects... and latest books: https://hannahfry.co.uk Her latest book (with Adam Rutherford) is the Complete Guide to Absolutely Everything (Abridged): https://amzn.to/30Mr6UE Hannah on Numberphile: http://bit.ly/hannah_vids Hannah on the Numberphile podcast: https://youtu.be/KKCjQWmUwv8 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Upgrade Your iPhone Experience

AI-recommended products based on this video

Loading...
BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

(7,876)
$11.99
FREE delivery Sat, Jun 14 on your first order
500+ bought in past month
Loading...
URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

(114)
$57.36$49.99
Prime$5.48 delivery Mon, Jun 16
Loading...
UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro

(4,725)
$31.99
500+ bought in past month
Loading...
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

(54,882)
$32.25
FREE delivery Mon, Aug 25 on your first order
1K+ bought in past month
Loading...
Magnetic Wireless Charger for iPhone: Fodable 3 in 1 Charging Station for Multiple Apple Devices - Travel Charging Pad Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus & Airpod Global Recycled Standard

Magnetic Wireless Charger for iPhone: Fodable 3 in 1 Charging Station for Multiple Apple Devices - Travel Charging Pad Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus & Airpod Global Recycled Standard

(656)
$49.99
PrimeFREE delivery Sat, Jun 14
100+ bought in past month
Loading...
Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

(750)
$59.99
PrimeFREE delivery Sat, Jun 14
Loading...
for Magsafe Car Mount【20 Strong Magnets 】Magnetic Phone Holder for Car Phone Holder Mount Dash【360°】Cell Phone Mount for Car Accessories,Car Mount for iPhone 16 Pro Max 15 14 13 12 Plus MagSafe Cases

for Magsafe Car Mount【20 Strong Magnets 】Magnetic Phone Holder for Car Phone Holder Mount Dash【360°】Cell Phone Mount for Car Accessories,Car Mount for iPhone 16 Pro Max 15 14 13 12 Plus MagSafe Cases

(11,563)
$16.98
FREE delivery Tue, Jun 17 on your first order
3K+ bought in past month
Loading...
BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

(7,876)
$11.99
FREE delivery Sat, Jun 14 on your first order
500+ bought in past month
Loading...
Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

(750)
$59.99
PrimeFREE delivery Sat, Jun 14
Loading...
4-in-1 Wireless Magnetic Power Bank 10800mAh Portable Charger with iWatch Charger, QC4.0+20W PD Fast Charging USB C Battery Pack for Magsafe, iPhone 16/15/14/13/12 Series, Apple Watch etc. (White)

4-in-1 Wireless Magnetic Power Bank 10800mAh Portable Charger with iWatch Charger, QC4.0+20W PD Fast Charging USB C Battery Pack for Magsafe, iPhone 16/15/14/13/12 Series, Apple Watch etc. (White)

(581)
$42.95
PrimeFREE delivery Sat, Jun 14
Loading...
eazpower for Magsafe Power Bank 10000mAh, Magnetic Battery Pack Wireless, 20W PD Fast Charging, Compact Portable Charger with Built-in Cables and Stand for iPhone 16/15/14/13/12/ Apple Watch/Airpods

eazpower for Magsafe Power Bank 10000mAh, Magnetic Battery Pack Wireless, 20W PD Fast Charging, Compact Portable Charger with Built-in Cables and Stand for iPhone 16/15/14/13/12/ Apple Watch/Airpods

(330)
$39.99
PrimeFREE delivery Sat, Jun 14
200+ bought in past month
Loading...
AMVR Upgraded Handle Attachment Compatible with Meta/Oculus Quest 3S/Quest 3 Accessories, 3-in-1 VR Gorilla Tag Long Arms, Beat Saber Handles, Golf Club Attachment(Not for Charging Dock)

AMVR Upgraded Handle Attachment Compatible with Meta/Oculus Quest 3S/Quest 3 Accessories, 3-in-1 VR Gorilla Tag Long Arms, Beat Saber Handles, Golf Club Attachment(Not for Charging Dock)

(183)
$29.99
FREE delivery Tue, Jun 17 on your first order
50+ bought in past month
Loading...
Spigen Case for iPhone 17 Case, Ultra Hybrid MagFit [Anti-Yellowing, Magsafe Compatible] Designed for Apple iPhone 17 Case (2025) - Clear White ClimatePartner certified

Spigen Case for iPhone 17 Case, Ultra Hybrid MagFit [Anti-Yellowing, Magsafe Compatible] Designed for Apple iPhone 17 Case (2025) - Clear White ClimatePartner certified

(2,190)
$18.99
FREE delivery Sat, Sep 20 on your first order
Loading...
Spigen Case for iPhone 16 Case, Ultra Hybrid [MagFit] Compatible with MagSafe - White

Spigen Case for iPhone 16 Case, Ultra Hybrid [MagFit] Compatible with MagSafe - White

(694)
$17.99
FREE delivery Sat, Jun 14 on your first order
100+ bought in past month
Loading...
Spigen Case for Galaxy S25 Plus Case, Ultra Hybrid S MagFit [Fast Wireless Charging] Compatible with MagSafe - White

Spigen Case for Galaxy S25 Plus Case, Ultra Hybrid S MagFit [Fast Wireless Charging] Compatible with MagSafe - White

(460)
$21.99
FREE delivery Sat, Jun 14 on your first order
50+ bought in past month
Loading...
Spigen Case for iPhone 15, iPhone 14, and iPhone 13, Ultra Hybrid MagFit Designed for Apple iPhone 15/14/13 - Crystal Clear

Spigen Case for iPhone 15, iPhone 14, and iPhone 13, Ultra Hybrid MagFit Designed for Apple iPhone 15/14/13 - Crystal Clear

(1,204)
$20.99
FREE delivery Sat, Sep 20 on your first order
100+ bought in past month
Loading...
MRGLAS 2025 Upgraded Magsafe Car Mount Vacuum Suction Magnetic Phone Holder Car, 360° Foldable Adjustable Suction Cup Phone Stand [89+LBS Suction & 2800gf Magnetic] for Car Accessories iPhone17/16

MRGLAS 2025 Upgraded Magsafe Car Mount Vacuum Suction Magnetic Phone Holder Car, 360° Foldable Adjustable Suction Cup Phone Stand [89+LBS Suction & 2800gf Magnetic] for Car Accessories iPhone17/16

(1,124)
$27.19
1K+ bought in past month
Loading...
OHLPRO Tablet Car Mount Universal Tablet Holder for Car Windshield Dash Dashboard, 360 Degree Rotation,TPU Suction Gel Stick, for iPad Mini 4/3/2/1Samsung Galaxy Size 7"- 10.5" Tablet Mount

OHLPRO Tablet Car Mount Universal Tablet Holder for Car Windshield Dash Dashboard, 360 Degree Rotation,TPU Suction Gel Stick, for iPad Mini 4/3/2/1Samsung Galaxy Size 7"- 10.5" Tablet Mount

(1,515)
$18.99
FREE delivery Tue, Jun 17 on your first order
Loading...
Magnetic Car Mount Air Vent Cell Phone Holder, Universal Vehicle Dash Dashboard Ac Airvent Cellphone Magic Stand with Clip Hook, for iPhone 16 15 Samsung Lenovo Google etc

Magnetic Car Mount Air Vent Cell Phone Holder, Universal Vehicle Dash Dashboard Ac Airvent Cellphone Magic Stand with Clip Hook, for iPhone 16 15 Samsung Lenovo Google etc

(128)
$21.99
FREE delivery Tue, Jun 17 on your first order
Loading...
AINOPE Phone Holder for Car Vent 2025 Gravity Air Vent Car Phone Holder Mount for iPhone 17 Pro Max Vent Clip Hand Free Cell Phone Car Mount for iPhone Air 17 16 Pro Max Samsung S25 Car Accesorries

AINOPE Phone Holder for Car Vent 2025 Gravity Air Vent Car Phone Holder Mount for iPhone 17 Pro Max Vent Clip Hand Free Cell Phone Car Mount for iPhone Air 17 16 Pro Max Samsung S25 Car Accesorries

(30,765)
$18.98
FREE delivery Sat, Jan 3 on your first order
2K+ bought in past month
Loading...
UGREEN USB to USB C Adapter & USB C to USB Adapter Combo 4-Pack, 10Gbps Type-C Converter, Car Charger Compatible with MacBook Pro, iPad Mac mini, iPhone 17/16, Galaxy, PC/Laptop, Hard Drive Enclosure

UGREEN USB to USB C Adapter & USB C to USB Adapter Combo 4-Pack, 10Gbps Type-C Converter, Car Charger Compatible with MacBook Pro, iPad Mac mini, iPhone 17/16, Galaxy, PC/Laptop, Hard Drive Enclosure

(86)
$9.74
Prime
Loading...
BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

(7,876)
$11.99
FREE delivery Sat, Jun 14 on your first order
500+ bought in past month
Loading...
URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

(114)
$57.36$49.99
Prime$5.48 delivery Mon, Jun 16
Loading...
UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro

(4,725)
$31.99
500+ bought in past month
Loading...
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

(54,882)
$32.25
FREE delivery Mon, Aug 25 on your first order
1K+ bought in past month
Loading...
Magnetic Wireless Charger for iPhone: Fodable 3 in 1 Charging Station for Multiple Apple Devices - Travel Charging Pad Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus & Airpod Global Recycled Standard

Magnetic Wireless Charger for iPhone: Fodable 3 in 1 Charging Station for Multiple Apple Devices - Travel Charging Pad Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus & Airpod Global Recycled Standard

(656)
$49.99
PrimeFREE delivery Sat, Jun 14
100+ bought in past month
Loading...
Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

(750)
$59.99
PrimeFREE delivery Sat, Jun 14
Loading...
for Magsafe Car Mount【20 Strong Magnets 】Magnetic Phone Holder for Car Phone Holder Mount Dash【360°】Cell Phone Mount for Car Accessories,Car Mount for iPhone 16 Pro Max 15 14 13 12 Plus MagSafe Cases

for Magsafe Car Mount【20 Strong Magnets 】Magnetic Phone Holder for Car Phone Holder Mount Dash【360°】Cell Phone Mount for Car Accessories,Car Mount for iPhone 16 Pro Max 15 14 13 12 Plus MagSafe Cases

(11,563)
$16.98
FREE delivery Tue, Jun 17 on your first order
3K+ bought in past month
Loading...
iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad

iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad

(4,036)
$8.99
FREE delivery Sun, Jun 29 on your first order
2K+ bought in past month