Igor Barani

Igor Barani works on typography, design and artificial intelligence. He writes mathematics in which every step carries its reason. His day job is radiation oncology.

Latest essay · 12 Nov 2026 Children who met their math minutes gained more. What does that prove?

0h Origin

The question

Where do you measure from?

The answer

From a place that anyone can name and find again. For the sky, it is the place where the Sun crosses the sky’s equator each March, and every star takes its address from there.

The sky is measured from where the Sun crosses its equator in March.

BecauseOnce a year, at the March equinox, the Sun crosses northward over the circle of sky above Earth’s equator, called the celestial equator. That crossing is named the first point of Aries, and any observer can watch for it and find it again. Angles east of it are counted in hours, 15° to the hour, and this site numbers its pages by that count, from 0h here to 7h.
The zero drifts, so every address in the sky carries a date.

BecauseThe Sun and the Moon pull on Earth’s bulging equator, so Earth’s axis swings around once in about 26,000 years. The celestial equator swings with it. So the crossing slides west by one degree every 72 years, a drift called precession. Hipparchus fixed the point in 130 BC at the edge of Aries, the Ram, and it now lies in the next constellation, Pisces. It can still be found again, because the Sun marks it afresh each March.
A letter is measured from the baseline.

BecauseNearly every letter in a line stands on it, so a ruler laid under any line of type finds it again. Heights are counted up from it and depths down, in thousandths of the type’s size. In Barani Sans the lowercase x rises 450, capitals rise 636, and descenders drop 186.
A radiosurgery plan is measured from a frame.

BecauseRadiosurgery aims radiation at a point inside the head, so each point needs an address, and a frame fixed to the skull supplies it. The Leksell frame sets its zero above, behind and to the right of the patient’s head, and its center at 100, 100, 100 millimeters. Every address in the head is then positive, with no minus sign to lose. Because the frame is fixed to the skull, its zero goes where the head goes and is found again in every scan.

Three zeros. The sky’s is where the Sun’s yearly path crosses the celestial equator heading north. The letter’s is the baseline of Barani Sans, with heights and depths in thousandths of the type’s size. The frame’s sits above, behind and to the patient’s right, which is on the left here because the box is seen from the front. The center then reads 100, 100, 100 mm. Schematic.

Another way

Measure from the observer instead, by how high a star stands above the horizon and in which compass direction.

BecauseThat address needs no atlas, but it changes every minute as the sky turns, and it differs from town to town. An atlas measures from the first point so that one address serves every observer.

Check

A zero that can be found again can be caught moving. At one degree every 72 years, the point has moved about 30° since 130 BC. Hipparchus’s point lay near the star Gamma Arietis, which should therefore stand about 30° east of today’s zero. The star’s cataloged address is 1h 54m east of the zero, which at 15° to the hour is 28.5°. Thirty were predicted and 28 found, where a cycle of 13,000 years would have put the star near 60°.

The test is loose by a few degrees, because Hipparchus’s point lay near the star and not on it. The three zeros are definitions, so they are certain, while the claim that a good zero must be findable is a judgment drawn from three cases. A zero in long use that its users could not find again would count against it.

KeepMeasure from a point you can find again.

Sources

Wikipedia. First point of Aries, for the March crossing, Hipparchus and the rate of drift. wikipedia.org.
Wikipedia. Axial precession, for its cause and its cycle of about 26,000 years. wikipedia.org.
Wikipedia. Right ascension, for hours counted east from the March crossing, 15° to the hour. wikipedia.org.
Wikipedia. Gamma Arietis, for its right ascension. wikipedia.org.
Wikipedia. Baseline (typography). wikipedia.org.
Schlesinger D. Historical and technical overview of Gamma Knife radiosurgery. AAPM Summer School, 2014, lecture handout. aapm.org.
Frohn O. d3-celestial, for the chart’s star positions and star names. github.com.
International Astronomical Union. Catalog of Star Names, as updated 4 April 2022. rochester.edu.
Wikipedia. 33 Arietis and 41 Arietis. wikipedia.org, wikipedia.org.

Igor Barani

Igor Barani designs type and figures, builds with artificial intelligence, writes about healthcare, and makes the With Every Reason mathematics books. By day he is a radiation oncologist who treats only tumors of the brain and spine. He is Professor and Chairman of Radiation Oncology at Barrow Neurological Institute in Phoenix, Arizona.

A note on the chart. The star names that come with d3-celestial, the open atlas behind this chart, list 33 Arietis as Barani. It is the faint ringed star in the Ram, northeast of Hamal. The International Astronomical Union’s catalog of star names does not list that name. In 2017 the Union gave the similar name Bharani, a lunar mansion of Hindu astronomy, to the neighboring star 41 Arietis.

Writing at 0h

Why is the first point of Aries still named for Aries? The first point of Aries keeps its name because the name marks a definition, the place where the Sun crosses the sky’s equator heading north, and that definition mentions no star, so it stayed true when the stars behind the point changed.

1h Typography

The question

How large must the type on a slide be for the back row to read it as easily as a book?

The answer

Large enough that each letter fills the same angle at a back-row eye as a book’s letter fills at reading distance. With the back row six screen-heights away, as an example, that is about 27-point type on a widescreen PowerPoint slide. The figure holds for a typeface whose lowercase x is half as tall as its point size.

Measure type by the angle it fills at the eye.

BecauseHow tall a letter looks is set by the angle between the lines of sight to its top and its foot. Twice as far away that angle halves, and the letter looks half as tall. So the angle is a measure that serves a page and a screen alike.
Take book type as the standard: its lowercase x fills about 0.24° at 40 cm.

BecauseNearly all the letters in a line of text are lowercase, so the height of the lowercase x sets how large the text looks. It is called the x-height. Legge and Bigelow measured the x-height in 200 hardcover and 100 paperback novels published since 2000. It averaged 0.24° at an assumed reading distance of 40 cm, which is about 1.7 mm on the page.
At six screen-heights, that angle spans 2.5% of the screen’s height.

BecauseAt 40 cm, 1.7 mm is about 1 part in 240 of the distance, and one angle spans the same share of any distance. Six screen-heights away, 1 part in 240 is 6 ÷ 240 = 2.5% of the screen’s height. The size of the hall drops out, because doubling both the screen and the distance leaves the angle unchanged.
On a slide, 2.5% of the height is 13.5 points.

BecauseA widescreen PowerPoint slide is 7.5 inches tall and a point is 1/72 of an inch, so the slide is 540 points tall. Of that, 2.5% is 13.5 points. In a typeface whose x-height is half its point size, an x-height of 13.5 points means 27-point type. For any hall, that comes to about 4.5 points for each screen-height between the screen and the back row.
Below about 23 points, a typical reader in that back row slows down.

BecauseBelow a certain size, reading slows sharply even for good eyes. The experiments that Legge and Bigelow review put that size at an x-height of about 0.2°, which from six screen-heights is about 23-point type. That size varies from about 0.15° to 0.3° with the reader, the typeface and the way it is measured. A reader who needs 0.3° is slowed by anything under 34 points, which is above the book standard itself.

The same angle at the eye. A book letter at 40 cm and a slide letter at the back row fill it equally. Not to scale.

Another way

Follow a fixed rule, and put nothing on a slide under 24 points.

BecauseSpeaker guidelines for scientific meetings give this rule, and it needs no arithmetic. At six screen-heights it lands just above the 23-point floor and three points short of the book standard. But a fixed size ignores the hall, and with the back row eight screen-heights away the floor itself rises to 30 points. The angle gives the rule its reason and says when to exceed it.

Check

Show a slide of 27-point text full screen on a laptop, and step back six times the height of the slide as shown. Hold a novel at 40 cm beside it. The two sets of lowercase letters should look about the same height. Novels run from 1.4 to 1.9 mm, so a small difference means nothing. Slide letters half the size of the book’s mean the arithmetic is wrong. The test also catches thin strokes and pale text, which the angle leaves out, though not the contrast that a lit room takes from a projector.

The geometry is certain and the standard is not, because 0.24° is what publishers print and no one has tested it as the best. The answer also leans on the typeface. At an x-height of 0.45 of the point size, the mean of the typefaces surveyed, the same angle needs 30 points. Reading speeds measured from the back of real halls would replace the standard.

KeepSize type by the angle at the back row.

Sources

Legge GE, Bigelow CA. Does print size matter for reading? A review of findings from vision science and typography. Journal of Vision 11(5):8, 2011. doi.org.
Microsoft Support. Change the size of your PowerPoint slides. microsoft.com.
Wikipedia. Point (typography), for the point as 1/72 of an inch. wikipedia.org.
American Statistical Association. Guidelines for preparing effective presentations, Joint Statistical Meetings 2015, for a minimum of 24 points. amstat.org.
ENAR. Guidelines for preparing effective presentations, 2025 Spring Meeting, for the same minimum. enar.org.

Type at work

Igor Barani is making a type family for the With Every Reason books. Barani Serif adapts EB Garamond, and Barani Sans adapts Hanken Grotesk, with forms that keep 1, l and I, and 0 and O, apart for children. He also sets his own slide system for scientific talks, and the themes of the editor in which he writes code.

This site is set in Barani Serif and Barani Sans, with Doto, a dot-matrix face by Óliver Lalan, for its labels.

Writing at 1h

2h Design

The question

A figure carries more ink than its data needs. What should go first?

The answer

Every mark the reader would not miss. Cover a mark, and if she can still read the same values and make the same comparison, it goes. Delete first, and refine only what is left.

Name every mark on the figure.

BecauseA mark is judged only once it is noticed, and the frame and grid that a program draws are the marks no one notices.
Ask of each mark what the reader would lose without it.

BecauseSome ink changes when the data change, as a line moves when a value does, and Edward Tufte called it the data-ink. All other ink stays the same whatever the numbers are, so it can earn its place only by helping her read the data-ink.
Delete the marks she would not miss.

BecauseThe box around the plot and the drop shadows would look the same for any data, so each draws the eye and tells it nothing. The markers repeat what the lines already show. The grid helps only a reader who must take exact values off the figure. This figure asks her to compare two trends, so the grid goes too.
Replace the legend with labels at the ends of the lines.

BecauseA legend makes the reader carry a color from the line to the key and a name back. A label on the line gives the name where her eye already is. The labels change with no data, and they stay because she would miss them.
Only now refine the weight, spacing and alignment of what remains.

BecauseWork spent refining a mark is lost if the mark is then deleted.

The same two series, before and after. The frame, grid, shadows and legend were deleted, and so were the markers, which repeated the lines. The only marks added were the labels A and B. Example data.

Another way

Keep the decoration.

BecauseIn one experiment, 20 people read decorated charts no less accurately than plain ones, and remembered them better two to three weeks later. So decoration can buy memory, and a figure meant to be remembered may earn its ornament. Readers preferred the decorated charts but read them no more accurately or quickly. So for a figure read beside its text, the answer stands.

Check

Run the test on the finished figure. Cover each remaining mark with a finger, and ask whether the reader could still read the same values and make the same comparison. If she could, that mark can go too. Then cover a line or a label, and the test must fail, or it is testing nothing.

The rule rests on the reasons above and not yet on a measurement. The one experiment cited here found plain charts read no more accurately than decorated ones. The rule also sets aside the reader who must take exact values from a figure, for whom a pale grid stays. A study in which readers misread stripped figures more often would overturn it.

KeepDelete first. Refine what is left.

Sources

Tufte ER. The Visual Display of Quantitative Information. Graphics Press, 1983. Its definition of data-ink is quoted at infovis-wiki.net.
Bateman S, Mandryk RL, Gutwin C, Genest A, McDine D, Brooks C. Useful junk? The effects of visual embellishment on comprehension and memorability of charts. Proceedings of CHI 2010, pages 2573–2582. mit.edu.

Design at work

Igor Barani holds his figures to the standard of a Nature review: uncluttered, labeled directly, and clear when projected for a room. He prefers drawn cross-sections and labeled cutaways to stock photographs. In his talks, medical images stay real scans; on this site they are drawn as labeled schematics.

Writing at 2h

How should a figure be drawn for the projector? A figure that looks sharp on a laptop fades on a projector because the room’s light falls on the screen and lifts its black, so it needs near-black ink, lines of 2 points or more on the slide, colors that differ in lightness and a name on every line.

3h Artificial intelligence

The question

A language model drafts the next step of a worked solution. How can a wrong step be stopped before anyone reads it?

The answer

Let the model propose and let the code decide. A checker computes the step’s numbers for itself, then passes the step on or sends it back. That stops a wrong number, and a wrong reason still needs a person.

Write down what a correct step must satisfy.

BecauseTake the step “eight needs two to make ten,” from 8 + 5. Its rule reads that the number needed must equal 10 − 8. A program can run a rule that exact, where a rule left in the model’s instructions is only a request.
Have the model return the step as typed fields: the claim, its numbers, its reason.

BecauseA typed field is a labeled slot for one kind of thing, such as a whole number. Code can then take the number from its slot without guessing. Software can guide a model as it writes, so that its output is guaranteed to fit the slots.
Check every number by computing it.

BecauseArithmetic has one right answer, and a program reaches it the same way every time, so a number that disagrees with the program is wrong.
When a step fails, ask once more, then use the step written by hand.

BecauseA model can reach its answer by a different path on each try, so a second try can pass where the first failed. A second failure suggests the fault is not chance, and more tries would then add delay and little else. The reader gets a step that a person wrote and checked beforehand, so no step with an unchecked number is shown.

The model proposes and the checker decides. A step that fails goes back once, and one that fails twice gives way to the step written by hand.

Another way

Have the model write a short program for the arithmetic, and let the computer run it.

BecauseLanguage models often slip in arithmetic even when they have set a problem up correctly, and a program that is run cannot slip that way. One research group built this under the name program-aided language models. It removes a wrong sum at its source, but the model still chooses which sum the step calls for, and that choice can be wrong. So the check on the finished step stays.

Check

Hand the checker one wrong step and one right one. For 8 + 5, “eight needs three to make ten” must come back rejected, because 10 − 8 = 2. “Eight needs two” must pass. A checker that passes both, or rejects both, has failed.

What the gate misses is everything code cannot compute. “Eight needs two, because two is even” has the right number and a wrong reason, and it passes. For numbers the gate is as certain as arithmetic, and for reasons it claims nothing. A wrong number that got through would change the answer, and so would a model whose errors lay mostly in its reasons.

KeepLet the model propose. Let the code decide.

Sources

Willard BT, Louf R. Efficient guided generation for large language models. arXiv 2307.09702, 2023. arxiv.org.
Gao L, Madaan A, Zhou S, et al. PAL, program-aided language models. arXiv 2211.10435, 2022. arxiv.org.
Wang X, Wei J, Schuurmans D, et al. Self-consistency improves chain of thought reasoning in language models. arXiv 2203.11171, 2022. arxiv.org.

Intelligence at work

Igor Barani builds multi-agent systems in Rust, with every step observable and written rules for what each agent may do. He also builds and runs the infrastructure they need.

Writing at 3h

In what form should an AI model hand its answer to code? When code must act on what a model has read, the model should answer in typed fields, such as a choice from a fixed list, a probability and a described score, which the code can check before it acts.

4h With Every Reason

The question

A child writes 8 + 5 = 13 but cannot say why. What is missing?

The answer

A reason for each step. The sum is a chain of three small claims, and each claim rests on something the child already knows.

Eight needs two to make ten.

BecauseNumbers are written in tens and ones, so the sum is easiest to write once one pile is a full ten. Eight and two make ten, a pair the child learned earlier, so eight is two short.
Take the two from the five, and three are left.

BecauseFive is two and three, so the five can give up two and keep three. The sticks only move from one pile to the other, and none is added or lost, so the sum is unchanged.
Ten and three is thirteen.

BecauseOne ten and three ones are written 13.

Sticks and a bundle, as in the wooden kit that comes with the books. Two sticks move from the five to finish the ten, which is then tied into a bundle.

Another way

Fill the five instead. Five needs five to make ten, so take five from the eight, and three are left. Ten and three is thirteen.

BecauseA pair to ten does the work again, from the other side. This way moves five sticks where the first way moved two, so filling the larger number takes fewer moves.

Check

Count on from eight, one count for each of the five: nine, ten, eleven, twelve, thirteen. Counting uses no pair to ten, so it reaches 13 by a second route.

The count checks the sum and not the child, who can count to thirteen and still not say why. To check the reason, ask for 8 + 6 or 7 + 5, and a child who holds it will make ten again. The sum is certain. That the reason is all that is missing is a reading of one child. It is wrong for a child who makes ten in the new sums and still cannot explain. That child had the reason and lacked only the words.

KeepFill the ten. Add what is left.

Sources

Givental A. Translator’s foreword to Kiselev’s Geometry, Book I, Planimetry. Sumizdat, 2006. sumizdat.org.
Schmittau J, Morris A. The development of algebra in the elementary mathematics curriculum of V.V. Davydov. The Mathematics Educator 8(1), 2004. nie.edu.sg.

With Every Reason

With Every Reason is a series of mathematics books by Igor Barani, published by KAGU, LLC. Its line is “Every answer, with a reason.” Every worked solution gives each step with its reason, in the manner of Andrei Kiselev’s textbooks. Each new idea opens with a problem the child’s present tools cannot finish, after the method of Vasily Davydov. A kit of wooden sticks and bundles comes with the books, so that the hands do each step before a word names it.

The series is planned as 21 books, from kindergarten through grade 12. The first books, kindergarten to grade 6, are in preparation.

The hour pages of this site are written the same way. Each gives a question, its answer, steps with their reasons, another way, a check, and one line to keep. The notes and essays are longer, and keep the answer first, the check, and the line to keep.

Writing at 4h

5h Healthcare

The question

A clinic is busy 90% of the time, and its patients still wait. Why do waits grow so fast as a service nears full?

The answer

Because a line of patients shrinks only in the clinic’s spare time, and a clinic near full has almost none. In the simplest model, the average patient at a clinic 90% busy waits nine times as long as a visit takes, and at 95%, nineteen.

The share of time the room is busy measures how full the clinic is.

BecauseTake a clinic with one room. Nine patients arrive in an hour, and the room could finish ten visits in an hour if it were never idle. The room is then busy nine-tenths of the time and spare for the remaining tenth.
Patients arrive in bunches, so a line forms well below full.

BecauseThree patients may come within ten minutes and none for the next twenty, so the line grows during the bunch. The idle minutes that follow cannot be saved for the next bunch, and they are lost.
The line shrinks only in the spare time.

BecauseAt 90% busy the room finishes ten visits for every nine arrivals, so a backlog shrinks by one patient in every ten visits. At 95% it shrinks by one in twenty, so the same bunch takes twice as long to clear.
In the simplest case, the wait is the busy share divided by the spare share.

BecauseTake arrivals at random and visits of uneven length, many short and a few long. The line builds during the busy share of the time and clears only in the spare share. For this case the patients ahead of a new arrival, counting the one being seen, average the busy share divided by the spare share. She waits one visit, on average, for each, even the one being seen, because such visits leave a whole visit still to run. That is 0.8 ÷ 0.2 = 4 visit-lengths at 80% busy, 9 at 90% and 19 at 95%.
The same five points cost six times as much near full.

BecauseFilling the room from 80% to 85% adds less than two visit-lengths to the wait, and filling it from 90% to 95% adds ten.

Average wait in line, in visit-lengths, against the share of time the room is busy. The upper curve has visits of uneven length, and the lower one has visits of fixed length.

Another way

Blame the variation instead of the fullness, and make every visit the same length.

BecauseWith visits of fixed length the wait is half as long. At 90% busy it is 4.5 visit-lengths in place of 9, with no new room and no new staff. But patients differ, so visits cannot all be alike, and the halved curve still reaches 9.5 at 95%.

Check

A simulation written for this page uses no formula. It draws random arrivals and visit lengths, and follows each patient through one room. Five runs of 2,000,000 patients each, at 90% busy, gave average waits of 8.97 to 9.25 visit-lengths, and 4.45 to 4.54 with fixed visits. Its 24 lines of Python can be saved and run to repeat the check.

The model leaves out extra rooms, patients who miss visits or give up, and appointments, which spread arrivals out. Booking appointments does not remove the line, which then forms in the calendar as a backlog. Green and Savin model that backlog as a one-room queue of this kind, with missed visits added. So the shape of the curve is firm, and its numbers belong to no real clinic. A clinic whose waits stayed flat as it filled from 80% to 95% would not fit the model.

KeepThe last few points of capacity cost the most waiting.

Sources

Wikipedia. M/M/1 queue, for the wait with random arrivals and varying visits. wikipedia.org.
Wikipedia. Exponential distribution, for the memoryless visit. wikipedia.org.
Wikipedia. M/D/1 queue, for the halved queue with visits of fixed length. wikipedia.org.
Green LV, Savin S. Reducing delays for medical appointments, a queueing approach. Operations Research 56(6):1526–1538, 2008. columbia.edu.

Healthcare at work

Igor Barani writes about healthcare from inside it, as a physician who also runs a department.

Writing at 5h

All writing filed under Healthcare

6h Practice

The question

A tumor sits a few millimeters from a nerve. How can the tumor receive a lethal dose while the nerve receives less than it can tolerate?

The answer

Aim beams from many directions, each too weak to harm what it crosses, and let them meet only at the tumor.

Give the tumor an address.

BecauseA beam can be aimed only at a point that has coordinates. A frame fixed to the skull, or a fitted mask checked by an X-ray scan on the machine, ties x, y and z to the head.
Read the address from images.

BecauseThe MRI and CT scans are taken with markers at known places on the frame, so every point in an image gets the frame’s coordinates. The tumor and the nerve then share one set of addresses.
Aim many beams, each too weak to harm what it crosses.

BecauseThe Gamma Knife Icon, a machine built for radiosurgery of the head, holds 192 sources of radioactive cobalt, and each sends one narrow beam. Tissue on any single path receives only that beam’s share, about half a percent of the dose at the crossing.
Let the beams cross only at the tumor.

BecauseDoses add where beams overlap, and all the beams overlap at only one point, so the full dose arrives only there. The figure labels that point the isocenter.
The dose falls away steeply at the edge of the crossing.

BecauseA few millimeters outside the crossing, most beams pass to one side of a point, so few overlap there and the dose drops. The nerve beside the tumor sits on that slope.

A slice through the head, seen from above, schematic. Sixteen beams are drawn where the Gamma Knife Icon has 192. Rings mark the dose falling away around the crossing. The address is an example in the frame’s coordinates.

Another way

Move one beam instead of fixing many. A linear accelerator makes one X-ray beam and turns it around the patient. The CyberKnife carries a small accelerator on a robotic arm from position to position.

BecauseBoth spread the directions over time instead of over sources. A moving beam can take more than 192 directions, but the machine must hold its aim as it moves, while fixed sources share one built-in focus. Either way there are many weak paths and one crossing, so the answer stands.

Check

Count beams instead of adding doses. Suppose beams 4 mm wide, the Icon’s narrowest setting, came evenly from every direction. A beam covers a point only if its center line passes within 2 mm of it. For a point 4 mm from the crossing, about one beam in eight does, a share of 1 − √(1 − (2/4)²) = 13%. In this model, then, a nerve 4 mm from the crossing receives about an eighth of the peak dose. By the same count the dose falls to half its peak 2.3 mm out. Measured on an Icon, it falls to half between 2.45 and 3.15 mm out, depending on direction.

The count leaves out each beam’s soft edge and scatter, so it predicts a sharper edge than the machine makes. The geometry is certain, and a patient’s numbers come from planning software and measurement, never from this sum. A measured dose still at half its peak a centimeter out would mean the crossing was not doing the work.

KeepWeak on every path. Strong at the crossing.

Sources

Maraghechi B, Kim T, Mitchell TJ, et al. Filmless quality assurance of a Leksell Gamma Knife Icon. Journal of Applied Clinical Medical Physics 22(1):59–67, 2021. doi.org.
Rojas-Villabona A, Miszkiel K, Kitchen N, et al. Evaluation of the stability of the stereotactic Leksell Frame G in Gamma Knife radiosurgery. Journal of Applied Clinical Medical Physics 17(3):75–89, 2016. doi.org.
Radiological Society of North America and American College of Radiology. Stereotactic radiosurgery (SRS) and stereotactic body radiotherapy (SBRT). radiologyinfo.org.
Wikipedia. Spherical cap, for the area formula behind the share of directions. wikipedia.org.

The day job

Igor Barani treats only tumors of the brain and spine, with the Gamma Knife, the CyberKnife and linear accelerators. At Barrow Neurological Institute in Phoenix he is Professor and Chairman of Radiation Oncology. His published work is listed on PubMed.

7h Correspondence

Letters

igor@barani.org

Patients and referring physicians should contact Barrow Neurological Institute directly. Medical questions cannot be answered through this address, because a letter cannot examine a patient.

Published work is listed on PubMed.

Sources

EB Garamond. github.com, github.com.
Hanken Grotesk. github.com.
Doto. github.com.
Frohn O. d3-celestial, for the star catalog and its year. github.com.
Wikipedia. Sidereal time. wikipedia.org.

Colophon

Set in Barani Serif 1.000 (release candidate 3, with the 0.500 italic) and Barani Sans 0.700. They adapt EB Garamond by Georg Duffner and Octavio Pardo, and Hanken Grotesk by Alfredo Marco Pradil. The labels are in Doto 1.000, a dot-matrix typeface by Óliver Lalan. Star positions come from the Hipparcos-based catalog in d3-celestial by Olaf Frohn, for the year 2000. The line on the opening page is computed in your browser from your device’s clock. It gives the local sidereal time in Phoenix, which is time kept by Earth’s turning against the stars. It also gives the height of the first point of Aries above the horizon there, ignoring the bending of light by the air. The pages run from 0h to 7h of right ascension, from the first point of Aries past the June solstice. As you turn the pages, the chart moves along the Sun’s yearly path.